-
question_answer1)
If the circles \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]and \[{{x}^{2}}+{{y}^{2}}-2gx+{{g}^{2}}-{{b}^{2}}=0\] touch each other externally, then
A)
\[g=ab\] done
clear
B)
\[{{g}^{2}}={{a}^{2}}+{{b}^{2}}\] done
clear
C)
\[{{g}^{2}}=ab\] done
clear
D)
\[g=a+b\] done
clear
View Solution play_arrow
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question_answer2)
For the given circles \[{{x}^{2}}+{{y}^{2}}-6x-2y+1=0\] and \[{{x}^{2}}+{{y}^{2}}+2x-8y+13=0\], which of the following is true [MP PET 1989]
A)
One circle lies inside the other done
clear
B)
One circle lies completely outside the other done
clear
C)
Two circle intersect in two points done
clear
D)
They touch each other done
clear
View Solution play_arrow
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question_answer3)
A circle passes through (0, 0) and (1, 0) and touches the circle \[{{x}^{2}}+{{y}^{2}}=9\], then the centre of circle is [IIT 1992]
A)
\[\left( \frac{3}{2},\frac{1}{2} \right)\] done
clear
B)
\[\left( \frac{1}{2},\frac{3}{2} \right)\] done
clear
C)
\[\left( \frac{1}{2},\frac{1}{2} \right)\] done
clear
D)
\[\left( \frac{1}{2},\ \pm \sqrt{2} \right)\] done
clear
View Solution play_arrow
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question_answer4)
If \[{{x}^{2}}+{{y}^{2}}+px+3y-5=0\] and \[{{x}^{2}}+{{y}^{2}}+5x\] \[+py+7=0\] cut orthogonally, then p is
A)
\[\frac{1}{2}\] done
clear
B)
1 done
clear
C)
\[\frac{3}{2}\] done
clear
D)
2 done
clear
View Solution play_arrow
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question_answer5)
The point of contact of the given circles \[{{x}^{2}}+{{y}^{2}}-6x-6y+10=0\] and \[{{x}^{2}}+{{y}^{2}}=2\], is
A)
(0, 0) done
clear
B)
(1, 1) done
clear
C)
(1, -1) done
clear
D)
(-1, -1) done
clear
View Solution play_arrow
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question_answer6)
From three non- collinear points we can draw [MP PET 1984; BIT Ranchi 1990]
A)
Only one circle done
clear
B)
Three circle done
clear
C)
Infinite circles done
clear
D)
No circle done
clear
View Solution play_arrow
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question_answer7)
The point (2, 3) is a limiting point of a coaxial system of circles of which \[{{x}^{2}}+{{y}^{2}}=9\]is a member. The co-ordinates of the other limiting point is given by [MP PET 1993]
A)
\[\left( \frac{18}{13},\frac{27}{13} \right)\] done
clear
B)
\[\left( \frac{9}{13},\frac{6}{13} \right)\] done
clear
C)
\[\left( \frac{18}{13},-\frac{27}{13} \right)\] done
clear
D)
\[\left( -\frac{18}{13},-\frac{9}{13} \right)\] done
clear
View Solution play_arrow
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question_answer8)
The equation of the circle having its centre on the line \[x+2y-3=0\]and passing through the points of intersection of the circles \[{{x}^{2}}+{{y}^{2}}-2x-4y+1=0\]and \[{{x}^{2}}+{{y}^{2}}-4x-2y+4=0\], is [MNR 1992]
A)
\[{{x}^{2}}+{{y}^{2}}-6x+7=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-3y+4=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-2x-2y+1=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}+2x-4y+4=0\] done
clear
View Solution play_arrow
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question_answer9)
If a circle passes through the point (1, 2) and cuts the circle \[{{x}^{2}}+{{y}^{2}}=4\] orthogonally, then the equation of the locus of its centre is [MNR 1992]
A)
\[{{x}^{2}}+{{y}^{2}}-3x-8y+1=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-2x-6y-7=0\] done
clear
C)
\[2x+4y-9=0\] done
clear
D)
\[2x+4y-1=0\] done
clear
View Solution play_arrow
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question_answer10)
Circles \[{{x}^{2}}+{{y}^{2}}-2x-4y=0\] and \[{{x}^{2}}+{{y}^{2}}-8y-4=0\] [IIT 1973]
A)
Touch each other internally done
clear
B)
Touch each other externally done
clear
C)
Cuts each other at two points done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer11)
The two circles \[{{x}^{2}}+{{y}^{2}}-4y=0\]and \[{{x}^{2}}+{{y}^{2}}-8y=0\] [BIT Ranchi 1985]
A)
Touch each other internally done
clear
B)
Touch each other externally done
clear
C)
Do not touch each other done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer12)
The equation of a circle passing through points of intersection of the circles \[{{x}^{2}}+{{y}^{2}}+13x-3y=0\]and \[2{{x}^{2}}+2{{y}^{2}}+4x-7y-25=0\]and point (1, 1) is [RPET 1988, 89; IIT 1983]
A)
\[4{{x}^{2}}+4{{y}^{2}}-30x-10y-25=0\] done
clear
B)
\[4{{x}^{2}}+4{{y}^{2}}+30x-13y-25=0\] done
clear
C)
\[4{{x}^{2}}+4{{y}^{2}}-17x-10y+25=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer13)
The locus of centre of a circle passing through (a, b) and cuts orthogonally to circle \[{{x}^{2}}+{{y}^{2}}={{p}^{2}}\], is [IIT 1988; AIEEE 2005]
A)
\[2ax+2by-({{a}^{2}}+{{b}^{2}}+{{p}^{2}})=0\] done
clear
B)
\[2ax+2by-({{a}^{2}}-{{b}^{2}}+{{p}^{2}})=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-3ax-4by+({{a}^{2}}+{{b}^{2}}-{{p}^{2}})=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-2ax-3by+({{a}^{2}}-{{b}^{2}}-{{p}^{2}})=0\] done
clear
View Solution play_arrow
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question_answer14)
The equation of the circle which intersects circles \[{{x}^{2}}+{{y}^{2}}+x+2y+3=0\],\[{{x}^{2}}+{{y}^{2}}+2x+4y+5=0\]and \[{{x}^{2}}+{{y}^{2}}-7x-8y-9=0\] at right angle, will be
A)
\[{{x}^{2}}+{{y}^{2}}-4x-4y-3=0\] done
clear
B)
\[3({{x}^{2}}+{{y}^{2}})+4x-4y-3=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+4x+4y-3=0\] done
clear
D)
\[3({{x}^{2}}+{{y}^{2}})+4(x+y)-3=0\] done
clear
View Solution play_arrow
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question_answer15)
The equation of the circle through the points of intersection of \[{{x}^{2}}+{{y}^{2}}-1=0\], \[{{x}^{2}}+{{y}^{2}}-2x-4y+1=0\] and touching the line \[x+2y=0\], is [Roorkee 1989]
A)
\[{{x}^{2}}+{{y}^{2}}+x+2y=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-x+20=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-x-2y=0\] done
clear
D)
\[2({{x}^{2}}+{{y}^{2}})-x-2y=0\] done
clear
View Solution play_arrow
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question_answer16)
If the circles \[{{x}^{2}}+{{y}^{2}}-9=0\]and \[{{x}^{2}}+{{y}^{2}}+2ax+2y+1=0\] touch each other, then a = [Roorkee Qualifying 1998]
A)
- 4/ 3 done
clear
B)
0 done
clear
C)
1 done
clear
D)
4/3 done
clear
View Solution play_arrow
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question_answer17)
The equation of the circle which passes through the origin, has its centre on the line \[x+y=4\]and cuts the circle \[{{x}^{2}}+{{y}^{2}}-4x+2y+4=0\]orthogonally, is
A)
\[{{x}^{2}}+{{y}^{2}}-2x-6y=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-6x-3y=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-4x-4y=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer18)
Two given circles \[{{x}^{2}}+{{y}^{2}}+ax+by+c=0\]and \[{{x}^{2}}+{{y}^{2}}+dx+ey+f=0\]will intersect each other orthogonally, only when
A)
\[a+b+c=d+e+f\] done
clear
B)
\[ad+be=c+f\] done
clear
C)
\[ad+be=2c+2f\] done
clear
D)
\[2ad+2be=c+f\] done
clear
View Solution play_arrow
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question_answer19)
The condition of the curves \[a{{x}^{2}}+b{{y}^{2}}=1\]and \[a'{{x}^{2}}+b'{{y}^{2}}=1\]to intersect each other orthogonally, is
A)
\[\frac{1}{a}-\frac{1}{a'}=\frac{1}{b}-\frac{1}{b'}\] done
clear
B)
\[\frac{1}{a}+\frac{1}{a'}=\frac{1}{b}+\frac{1}{b'}\] done
clear
C)
\[\frac{1}{a}+\frac{1}{b}=\frac{1}{a'}+\frac{1}{b'}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer20)
The radical centre of the circles \[{{x}^{2}}+{{y}^{2}}+4x+6y=19,{{x}^{2}}+{{y}^{2}}=9\]and \[{{x}^{2}}+{{y}^{2}}-2x-2y=5\]will be
A)
(1, 1) done
clear
B)
(-1, 1) done
clear
C)
(1, -1) done
clear
D)
(0, 1) done
clear
View Solution play_arrow
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question_answer21)
The locus of the centres of the circles which touch externally the circles \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]and \[{{x}^{2}}+{{y}^{2}}=4ax\], will be
A)
\[12{{x}^{2}}-4{{y}^{2}}-24ax+9{{a}^{2}}=0\] done
clear
B)
\[12{{x}^{2}}+4{{y}^{2}}-24ax+9{{a}^{2}}=0\] done
clear
C)
\[12{{x}^{2}}-4{{y}^{2}}+24ax+9{{a}^{2}}=0\] done
clear
D)
\[12{{x}^{2}}+4{{y}^{2}}+24ax+9{{a}^{2}}=0\] done
clear
View Solution play_arrow
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question_answer22)
If the circles of same radius a and centers at (2, 3) and (5, 6) cut orthogonally, then a = [EAMCET 1988]
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
View Solution play_arrow
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question_answer23)
The equation of a circle passing through origin and co-axial to circles \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] and \[{{x}^{2}}+{{y}^{2}}+2ax=2{{a}^{2}},\] is
A)
\[{{x}^{2}}+{{y}^{2}}=1\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+2ax=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-2ax=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}=2{{a}^{2}}\] done
clear
View Solution play_arrow
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question_answer24)
The equation of the circle which passes through the point of intersection of circles \[{{x}^{2}}+{{y}^{2}}-8x-2y+7=0\] and \[{{x}^{2}}+{{y}^{2}}-4x+10y+8=0\] and having its centre on\[y\]-axis, will be
A)
\[{{x}^{2}}+{{y}^{2}}+22x+9=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+22x-9=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+22y+9=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}+22y-9=0\] done
clear
View Solution play_arrow
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question_answer25)
The equation of line passing through the points of intersection of the circles \[3{{x}^{2}}+3{{y}^{2}}-2x+12y-9=0\] and \[{{x}^{2}}+{{y}^{2}}+6x+2y-15=0\], is [IIT 1986; UPSEAT 1999]
A)
\[10x-3y-18=0\] done
clear
B)
\[10x+3y-18=0\] done
clear
C)
\[10x+3y+18=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer26)
From any point on the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] tangents are drawn to the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}{{\sin }^{2}}\alpha \], the angle between them is [RPET 2002]
A)
\[\frac{\alpha }{2}\] done
clear
B)
\[\alpha \] done
clear
C)
\[2\alpha \] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer27)
The equation of the circle through the point of intersection of the circles \[{{x}^{2}}+{{y}^{2}}-8x-2y+7=0\], \[{{x}^{2}}+{{y}^{2}}-4x+10y+8=0\] and (3, -3) is
A)
\[23{{x}^{2}}+23{{y}^{2}}-156x+38y+168=0\] done
clear
B)
\[23{{x}^{2}}+23{{y}^{2}}+156x+38y+168=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+156x+38y+168=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer28)
The equation of circle which passes through the point (1,1) and intersect the given circles \[{{x}^{2}}+{{y}^{2}}+2x+4y+6=0\] and \[{{x}^{2}}+{{y}^{2}}+4x+6y+2=0\] orthogonally, is
A)
\[{{x}^{2}}+{{y}^{2}}+16x+12y+2=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-16x-12y-2=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-16x+12y+2=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer29)
Two circles \[{{S}_{1}}={{x}^{2}}+{{y}^{2}}+2{{g}_{1}}x+2{{f}_{1}}y+{{c}_{1}}=0\] and \[{{S}_{2}}={{x}^{2}}+{{y}^{2}}+2{{g}_{2}}x+2{{f}_{2}}y+{{c}_{2}}=0\]cut each other orthogonally, then [RPET 1995]
A)
\[2{{g}_{1}}{{g}_{2}}+2{{f}_{1}}{{f}_{2}}={{c}_{1}}+{{c}_{2}}\] done
clear
B)
\[2{{g}_{1}}{{g}_{2}}-2{{f}_{1}}{{f}_{2}}={{c}_{1}}+{{c}_{2}}\] done
clear
C)
\[2{{g}_{1}}{{g}_{2}}+2{{f}_{1}}{{f}_{2}}={{c}_{1}}-{{c}_{2}}\] done
clear
D)
\[2{{g}_{1}}{{g}_{2}}-2{{f}_{1}}{{f}_{2}}={{c}_{1}}-{{c}_{2}}\] done
clear
View Solution play_arrow
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question_answer30)
Circles \[{{x}^{2}}+{{y}^{2}}+2gx+2fy=0\] and \[{{x}^{2}}+{{y}^{2}}\] \[+2g'x+2f'y=\] \[0\] touch externally, if [MP PET 1994; Karnataka CET 2003]
A)
\[f'g=g'f\] done
clear
B)
\[fg=f'g'\] done
clear
C)
\[f'g'+fg=0\] done
clear
D)
\[f'g+g'f=0\] done
clear
View Solution play_arrow
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question_answer31)
The two circles \[{{x}^{2}}+{{y}^{2}}-2x-3=0\]and \[{{x}^{2}}+{{y}^{2}}-4x-6y-8=0\]are such that [MNR 1995]
A)
They touch each other done
clear
B)
They intersect each other done
clear
C)
One lies inside the other done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer32)
One of the limit point of the coaxial system of circles containing \[{{x}^{2}}+{{y}^{2}}-6x-6y+4=0\], \[{{x}^{2}}+{{y}^{2}}-2x\] \[-4y+3=0\] is [EAMCET 1987]
A)
\[(-1,\,1)\] done
clear
B)
\[(-1,\,2)\] done
clear
C)
\[(-2,\,1)\] done
clear
D)
\[(-2,\,2)\] done
clear
View Solution play_arrow
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question_answer33)
The equation of the circle having the lines \[{{x}^{2}}+2xy+3x+6y=0\]as its normals and having size just sufficient to contain the circle \[x(x-4)+y(y-3)=0\]is [Roorkee 1990]
A)
\[{{x}^{2}}+{{y}^{2}}+3x-6y-40=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+6x-3y-45=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+8x+4y-20=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}+4x+8y+20=0\] done
clear
View Solution play_arrow
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question_answer34)
Locus of the point, the difference of the squares of lengths of tangents drawn from which to two given circles is constant, is
A)
Circle done
clear
B)
Parabola done
clear
C)
Straight line done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer35)
Consider the circles\[{{x}^{2}}+{{(y-1)}^{2}}=\] \[9,{{(x-1)}^{2}}+{{y}^{2}}=25\]. They are such that [EAMCET 1994]
A)
These circles touch each other done
clear
B)
One of these circles lies entirely inside the other done
clear
C)
Each of these circles lies outside the other done
clear
D)
They intersect in two points done
clear
View Solution play_arrow
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question_answer36)
The locus of centre of the circle which cuts the circles\[{{x}^{2}}+{{y}^{2}}+2{{g}_{1}}x+2{{f}_{1}}y+{{c}_{1}}=0\]and\[{{x}^{2}}+{{y}^{2}}+2{{g}_{2}}x+2{{f}_{2}}y+{{c}_{2}}=0\]orthogonally is [Karnataka CET 1991]
A)
An ellipse done
clear
B)
The radical axis of the given circles done
clear
C)
A conic done
clear
D)
Another circle done
clear
View Solution play_arrow
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question_answer37)
A circle passes through the origin and has its centre on \[y=x\]. If it cuts \[{{x}^{2}}+{{y}^{2}}-4x-6y+10=0\] orthogonally, then the equation of the circle is [EAMCET 1994]
A)
\[{{x}^{2}}+{{y}^{2}}-x-y=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-6x-4y=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-2x-2y=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}+2x+2y=0\] done
clear
View Solution play_arrow
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question_answer38)
The radical centre of three circles described on the three sides of a triangle as diameter is [EAMCET 1994]
A)
The orthocentre done
clear
B)
The circumcentre done
clear
C)
The incentre of the triangle done
clear
D)
The centroid done
clear
View Solution play_arrow
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question_answer39)
The lengths of tangents from a fixed point to three circles of coaxial system are \[{{t}_{1}},{{t}_{2}},{{t}_{3}}\]and if P, Q and R be the centres, then \[QRt_{1}^{2}+RPt_{2}^{2}+PQt_{3}^{2}\]is equal to
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
0 done
clear
View Solution play_arrow
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question_answer40)
P, Q and R are the centres and \[{{r}_{1}},\,\,{{r}_{2}},\,\,{{r}_{3}}\] are the radii respectively of three co-axial circles, then \[QRr_{1}^{2}+RP\,r_{2}^{2}+PQr_{3}^{2}\] is equal to
A)
\[PQ\ .\,QR\,.\,RP\] done
clear
B)
\[-PQ\,.\,QR\,.\,RP\] done
clear
C)
\[P{{Q}^{2}}.Q{{R}^{2}}.R{{P}^{2}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer41)
The circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\]bisects the circumference of the circle \[{{x}^{2}}+{{y}^{2}}+2g'x+2f'y+c'=0\], if
A)
\[2g'(g-g')+2f'(f-f')=c-c'\] done
clear
B)
\[g'(g-g')+f'(f-f')=c-c'\] done
clear
C)
\[f(g-g')+g(f-f')=c-c'\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer42)
Circles \[{{(x+a)}^{2}}+{{(y+b)}^{2}}={{a}^{2}}\] and \[{{(x+\alpha )}^{2}}\] \[+{{(y+\beta )}^{2}}=\]\[{{\beta }^{2}}\] cut orthogonally, if
A)
\[a\alpha +b\beta ={{b}^{2}}+{{\alpha }^{2}}\] done
clear
B)
\[2(a\alpha +b\beta )={{b}^{2}}+{{\alpha }^{2}}\] done
clear
C)
\[a\alpha +b\beta ={{a}^{2}}+{{b}^{2}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer43)
The circles \[{{x}^{2}}+{{y}^{2}}+4x+6y+3=0\] and \[2({{x}^{2}}+{{y}^{2}})+6x+4y+C=0\] will cut orthogonally, if C equals [Kurukshetra CEE 1996]
A)
4 done
clear
B)
18 done
clear
C)
12 done
clear
D)
16 done
clear
View Solution play_arrow
-
question_answer44)
Any circle through the point of intersection of the lines \[x+\sqrt{3}y=1\] and \[\sqrt{3}x-y=2\]if intersects these lines at points P and Q, then the angle subtended by the arc PQ at its centre is [MP PET 1998]
A)
\[{{180}^{o}}\] done
clear
B)
\[{{90}^{o}}\] done
clear
C)
\[{{120}^{o}}\] done
clear
D)
Depends on centre and radius done
clear
View Solution play_arrow
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question_answer45)
The equation of a circle that intersects the circle \[{{x}^{2}}+{{y}^{2}}+14x+6y+2=0\]orthogonally and whose centre is (0, 2) is [MP PET 1998]
A)
\[{{x}^{2}}+{{y}^{2}}-4y-6=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+4y-14=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+4y+14=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-4y-14=0\] done
clear
View Solution play_arrow
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question_answer46)
If the circles \[{{x}^{2}}+{{y}^{2}}=4,{{x}^{2}}+{{y}^{2}}-10x+\lambda =0\] touch externally, then \[\lambda \]is equal to [AMU 1999]
A)
-16 done
clear
B)
9 done
clear
C)
16 done
clear
D)
25 done
clear
View Solution play_arrow
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question_answer47)
In the co-axial system of circle \[{{x}^{2}}+{{y}^{2}}+2gx+c=0\], where g is a parameter, if \[c>0\] then the circles are [Karnataka CET 1999]
A)
Orthogonal done
clear
B)
Touching type done
clear
C)
Intersecting type done
clear
D)
Non-intersecting type done
clear
View Solution play_arrow
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question_answer48)
If the straight line \[y=mx\]is outside the circle\[{{x}^{2}}+{{y}^{2}}-20y+90=0\], then [Roorkee 1999]
A)
\[m>3\] done
clear
B)
\[m<3\] done
clear
C)
\[|m|>3\] done
clear
D)
\[|m|<3\] done
clear
View Solution play_arrow
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question_answer49)
The equation of radical axis of the circles \[2{{x}^{2}}+2{{y}^{2}}-7x=0\] and \[{{x}^{2}}+{{y}^{2}}-4y-7=0\] is [RPET 1996]
A)
\[7x+8y+14=0\] done
clear
B)
\[7x-8y+14=0\] done
clear
C)
\[7x-8y-14=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer50)
The equation of the circle which passes through the intersection of \[{{x}^{2}}+{{y}^{2}}+13x-3y=0\]and \[2{{x}^{2}}+2{{y}^{2}}+4x-7y-25=0\] and whose centre lies on \[13x+30y=0\] is [DCE 2001]
A)
\[{{x}^{2}}+{{y}^{2}}+30x-13y-25=0\] done
clear
B)
\[4{{x}^{2}}+4{{y}^{2}}+30x-13y-25=0\] done
clear
C)
\[2{{x}^{2}}+2{{y}^{2}}+30x-13y-25=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}+30x-13y+25=0\] done
clear
View Solution play_arrow
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question_answer51)
The radical centre of the circles \[{{x}^{2}}+{{y}^{2}}-16x+60=0,\,{{x}^{2}}+{{y}^{2}}-12x+27=0,\] \[{{x}^{2}}+{{y}^{2}}-12y+8=0\] is [RPET 2000]
A)
(13, 33/4) done
clear
B)
(33/4, -13) done
clear
C)
(33/4, 13) done
clear
D)
None of these done
clear
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question_answer52)
The radical axis of two circles and the line joining their centres are [Karnataka CET 2001]
A)
Parallel done
clear
B)
Perpendicular done
clear
C)
Neither parallel, nor perpendicular done
clear
D)
Intersecting, but not fully perpendicular done
clear
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question_answer53)
The two circles \[{{x}^{2}}+{{y}^{2}}-2x+6y+6=0\] and \[{{x}^{2}}+{{y}^{2}}-5x+6y+15=0\] [Karnataka CET 2001]
A)
Intersect done
clear
B)
Are concentric done
clear
C)
Touch internally done
clear
D)
Touch externally done
clear
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question_answer54)
The locus of the centre of a circle which cuts orthogonally the circle \[{{x}^{2}}+{{y}^{2}}-20x+4=0\] and which touches \[x=2\] is [UPSEAT 2001]
A)
\[{{y}^{2}}=16x+4\] done
clear
B)
\[{{x}^{2}}=16y\] done
clear
C)
\[{{x}^{2}}=16y+4\] done
clear
D)
\[{{y}^{2}}=16x\] done
clear
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question_answer55)
The locus of the centre of circle which cuts the circles \[{{x}^{2}}+{{y}^{2}}+4x-6y+9=0\] and \[{{x}^{2}}+{{y}^{2}}-4x+6y+4=0\] orthogonally is [UPSEAT 2001]
A)
\[12x+8y+5=0\] done
clear
B)
\[8x+12y+5=0\] done
clear
C)
\[8x-12y+5=0\] done
clear
D)
None of these done
clear
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question_answer56)
Radical axis of the circles \[3{{x}^{2}}+3{{y}^{2}}-7x+8y+11=0\] and \[{{x}^{2}}+{{y}^{2}}-3x-4y+5=0\] is [RPET 2001]
A)
\[x+10y+2=0\] done
clear
B)
\[x+10y-2=0\] done
clear
C)
\[x+10y+8=0\] done
clear
D)
\[x+10y-8=0\] done
clear
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question_answer57)
If the chord \[y=mx+1\] of the circle \[{{x}^{2}}+{{y}^{2}}=1\] subtends an angle of measure \[{{45}^{o}}\] at the major segment of the circle then value of m is [AIEEE 2002]
A)
2 done
clear
B)
- 2 done
clear
C)
- 1 done
clear
D)
None of these done
clear
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question_answer58)
If the two circles \[2{{x}^{2}}+2{{y}^{2}}-3x+6y+k=0\] and \[{{x}^{2}}+{{y}^{2}}-4x+10y+16=0\] cut orthogonally, then the value of k is [Kerala (Engg.) 2002]
A)
41 done
clear
B)
14 done
clear
C)
4 done
clear
D)
0 done
clear
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question_answer59)
The centre of the circle, which cuts orthogonally each of the three circles \[{{x}^{2}}+{{y}^{2}}+2x+17y+4=0,\] \[{{x}^{2}}+{{y}^{2}}+7x+6y+11=0,\] \[{{x}^{2}}+{{y}^{2}}-x+22y+3=0\] is [MP PET 2003]
A)
(3, 2) done
clear
B)
(1, 2) done
clear
C)
(2, 3) done
clear
D)
(0, 2) done
clear
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question_answer60)
Equation of radical axis of the circles \[{{x}^{2}}+{{y}^{2}}-3x-4y+5=0\], \[2{{x}^{2}}+2{{y}^{2}}-10x\]\[-12y+12=0\] is [RPET 2003]
A)
\[2x+2y-1=0\] done
clear
B)
\[2x+2y+1=0\] done
clear
C)
\[x+y+7=0\] done
clear
D)
\[x+y-7=0\] done
clear
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question_answer61)
If the circle \[{{x}^{2}}+{{y}^{2}}+6x-2y+k=0\] bisects the circumference of the circle \[{{x}^{2}}+{{y}^{2}}+2x-6y-15=0,\] then k = [EAMCET 2003]
A)
21 done
clear
B)
- 21 done
clear
C)
23 done
clear
D)
- 23 done
clear
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question_answer62)
If P is a point such that the ratio of the squares of the lengths of the tangents from P to the circles\[{{x}^{2}}+{{y}^{2}}+2x-4y-20=0\] and \[{{x}^{2}}+{{y}^{2}}-4x+2y-44=0\] is 2 : 3, then the locus of P is a circle with centre [EAMCET 2003]
A)
(7, - 8) done
clear
B)
(- 7, 8) done
clear
C)
(7, 8) done
clear
D)
(- 7, - 8) done
clear
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question_answer63)
If two circles \[{{(x-1)}^{2}}+{{(y-3)}^{2}}={{r}^{2}}\] and \[{{x}^{2}}+{{y}^{2}}-8x+2y+8=0\] intersect in two distinct points, then [IIT 1989; Karnataka CET 2002; DCE 2000, 01; AIEEE 2003; MP PET 2004]
A)
\[2<r<8\] done
clear
B)
\[r=2\] done
clear
C)
\[r<2\] done
clear
D)
\[r>2\] done
clear
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question_answer64)
The points of intersection of the circles \[{{x}^{2}}+{{y}^{2}}=25\]and \[{{x}^{2}}+{{y}^{2}}-8x+7=0\]are [MP PET 1988]
A)
(4, 3) and (4, -3) done
clear
B)
(4, -3) and (-4, -3) done
clear
C)
(-4, 3) and (4, 3) done
clear
D)
(4, 3) and (3, 4) done
clear
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question_answer65)
If circles \[{{x}^{2}}+{{y}^{2}}+2ax+c=0\]and \[{{x}^{2}}+{{y}^{2}}+2by+c=0\] touch each other, then [MNR 1987]
A)
\[\frac{1}{a}+\frac{1}{b}=\frac{1}{c}\] done
clear
B)
\[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{{{c}^{2}}}\] done
clear
C)
\[\frac{1}{a}+\frac{1}{b}={{c}^{2}}\] done
clear
D)
\[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{c}\] done
clear
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question_answer66)
If d is the distance between the centres of two circles, \[{{r}_{1}},{{r}_{2}}\]are their radii and \[d={{r}_{1}}+{{r}_{2}}\], then [MP PET 1986]
A)
The circles touch each other externally done
clear
B)
The circles touch each other internally done
clear
C)
The circles cut each other done
clear
D)
The circles are disjoint done
clear
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question_answer67)
The points of intersection of circles \[{{x}^{2}}+{{y}^{2}}=2ax\] and \[{{x}^{2}}+{{y}^{2}}=2by\] are [AMU 2000]
A)
(0, 0), (a, b) done
clear
B)
(0, 0), \[\left( \frac{2a{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}},\frac{2b{{a}^{2}}}{{{a}^{2}}+{{b}^{2}}} \right)\] done
clear
C)
(0, 0), \[\left( \frac{{{a}^{2}}+{{b}^{2}}}{{{a}^{2}}},\frac{{{a}^{2}}+{{b}^{2}}}{{{b}^{2}}} \right)\] done
clear
D)
None of the above done
clear
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question_answer68)
A circle with radius 12 lies in the first quadrant and touches both the axes, another circle has its centre at (8,9) and radius 7. Which of the following statements is true
A)
Circles touch each other internally done
clear
B)
Circles touch each other externally done
clear
C)
Circles intersect at two distinct points done
clear
D)
None of these done
clear
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question_answer69)
The equation of radical axis of the circles \[{{x}^{2}}+{{y}^{2}}+x-y+2=0\] and \[3{{x}^{2}}+3{{y}^{2}}-4x-12=0,\]is [RPET 1984, 85, 86, 91, 2000]
A)
\[2{{x}^{2}}+2{{y}^{2}}-5x+y-14=0\] done
clear
B)
\[7x-3y+18=0\] done
clear
C)
\[5x-y+14=0\] done
clear
D)
None of these done
clear
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question_answer70)
If the centre of a circle which passing through the points of intersection of the circles \[{{x}^{2}}+{{y}^{2}}-6x+2y+4=0\]and \[{{x}^{2}}+{{y}^{2}}+2x-4y-6=0\]is on the line \[y=x\], then the equation of the circle is [RPET 1991; Roorkee 1989]
A)
\[7{{x}^{2}}+7{{y}^{2}}-10x+10y-11=0\] done
clear
B)
\[7{{x}^{2}}+7{{y}^{2}}+10x-10y-12=0\] done
clear
C)
\[7{{x}^{2}}+7{{y}^{2}}-10x-10y-12=0\] done
clear
D)
\[7{{x}^{2}}+7{{y}^{2}}-10x-12=0\] done
clear
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question_answer71)
If the circles \[{{x}^{2}}+{{y}^{2}}-2ax+c=0\] and \[{{x}^{2}}+{{y}^{2}}+2by+2\lambda =0\] intersect orthogonally, then the value of \[\lambda \]is
A)
c done
clear
B)
- c done
clear
C)
0 done
clear
D)
None of these done
clear
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question_answer72)
The radical axis of the pair of circle \[{{x}^{2}}+{{y}^{2}}=144\]and \[{{x}^{2}}+{{y}^{2}}-15x+12y=0\]is
A)
\[15x-12y=0\] done
clear
B)
\[3x-2y=12\] done
clear
C)
\[5x-4y=48\] done
clear
D)
None of these done
clear
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question_answer73)
The condition that the circle \[{{(x-3)}^{2}}+{{(y-4)}^{2}}={{r}^{2}}\]lies entirely within the circle \[{{x}^{2}}+{{y}^{2}}={{R}^{2}},\]is [AMU 1999]
A)
\[R+r\le 7\] done
clear
B)
\[{{R}^{2}}+{{r}^{2}}<49\] done
clear
C)
\[{{R}^{2}}-{{r}^{2}}<25\] done
clear
D)
\[R-r>5\] done
clear
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question_answer74)
The value of \[\lambda \], for which the circle \[{{x}^{2}}+{{y}^{2}}+2\lambda x+6y+1=0\], intersects the circle \[{{x}^{2}}+{{y}^{2}}+4x+2y=0\]orthogonally is [MP PET 2004]
A)
\[\frac{-5}{2}\] done
clear
B)
\[-1\] done
clear
C)
\[\frac{-11}{8}\] done
clear
D)
\[\frac{-5}{4}\] done
clear
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question_answer75)
The value of k so that \[{{x}^{2}}+{{y}^{2}}+kx+4y+2=0\] and \[2({{x}^{2}}+{{y}^{2}})-4x-3y+k=0\]cut orthogonally is [Karnataka CET 2004]
A)
\[\frac{10}{3}\] done
clear
B)
\[\frac{-8}{3}\] done
clear
C)
\[\frac{-10}{3}\] done
clear
D)
\[\frac{8}{3}\] done
clear
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question_answer76)
If the circles \[{{x}^{2}}+{{y}^{2}}+2ax+cy+a=0\] and \[{{x}^{2}}+{{y}^{2}}-3ax+dy-1=0\] intersect in two distinct points \[P\] and \[Q\] then the line \[5x+by-a=0\] passes through \[P\] and \[Q\] for [AIEEE 2005]
A)
Infinitely many values of \[a\] done
clear
B)
Exactly two values of \[a\] done
clear
C)
Exactly one value of \[a\] done
clear
D)
No value of \[a\] done
clear
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question_answer77)
The two circles \[{{x}^{2}}+{{y}^{2}}-2x+22y+5=0\] and \[{{x}^{2}}+{{y}^{2}}+14x+6y+k=0\] intersect orthogonally provided k is equal to [Karnataka CET 2005]
A)
47 done
clear
B)
\[-47\] done
clear
C)
49 done
clear
D)
\[-\text{ }49\] done
clear
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question_answer78)
A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is [AIEEE 2005]
A)
A hyperbola done
clear
B)
A parabola done
clear
C)
An ellipse done
clear
D)
A circle done
clear
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