-
question_answer1)
The common chord of the circle \[{{x}^{2}}+{{y}^{2}}+4x+1=0\] and \[{{x}^{2}}+{{y}^{2}}+6x+2y+3=0\] is [MP PET 1991]
A)
\[x+y+1=0\] done
clear
B)
\[5x+y+2=0\] done
clear
C)
\[2x+2y+5=0\] done
clear
D)
\[3x+y+3=0\] done
clear
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question_answer2)
If the middle point of a chord of the circle \[{{x}^{2}}+{{y}^{2}}+x-y-1=0\]be (1, 1), then the length of the chord is
A)
4 done
clear
B)
2 done
clear
C)
5 done
clear
D)
None of these done
clear
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question_answer3)
\[y=mx\] is a chord of a circle of radius a and the diameter of the circle lies along x-axis and one end of this chord in origin .The equation of the circle described on this chord as diameter is [MP PET 1990]
A)
\[(1+{{m}^{2}})({{x}^{2}}+{{y}^{2}})-2ax=0\] done
clear
B)
\[(1+{{m}^{2}})({{x}^{2}}+{{y}^{2}})-2a(x+my)=0\] done
clear
C)
\[(1+{{m}^{2}})({{x}^{2}}+{{y}^{2}})+2a(x+my)=0\] done
clear
D)
\[(1+{{m}^{2}})({{x}^{2}}+{{y}^{2}})-2a(x-my)=0\] done
clear
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question_answer4)
The locus of the middle points of those chords of the circle \[{{x}^{2}}+{{y}^{2}}=4\]which subtend a right angle at the origin is [MP PET 1990; IIT 1984; RPET 1997; DCE 2000, 01]
A)
\[{{x}^{2}}+{{y}^{2}}-2x-2y=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}=4\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}=2\] done
clear
D)
\[{{(x-1)}^{2}}+{{(y-2)}^{2}}=5\] done
clear
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question_answer5)
The equation of the chord of the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]having \[({{x}_{1}},{{y}_{1}})\]as its mid-point is [IIT 1983; MP PET 1986; Pb. CET 2003]
A)
\[x{{y}_{1}}+y{{x}_{1}}={{a}^{2}}\] done
clear
B)
\[{{x}_{1}}+{{y}_{1}}=a\] done
clear
C)
\[x{{x}_{1}}+y{{y}_{1}}=x_{1}^{2}+y_{1}^{2}\] done
clear
D)
\[x{{x}_{1}}+y{{y}_{1}}={{a}^{2}}\] done
clear
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question_answer6)
Locus of the middle points of the chords of the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]which are parallel to \[y=2x\] will be
A)
A circle with radius a done
clear
B)
A straight line with slope \[-\frac{1}{2}\] done
clear
C)
A circle will centre (0, 0) done
clear
D)
A straight line with slope - 2 done
clear
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question_answer7)
The length of the chord intercepted by the circle \[{{x}^{2}}+{{y}^{2}}={{r}^{2}}\]on the line \[\frac{x}{a}+\frac{y}{b}=1\] is
A)
\[\sqrt{\frac{{{r}^{2}}({{a}^{2}}+{{b}^{2}})-{{a}^{2}}{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}}\] done
clear
B)
\[2\sqrt{\frac{{{r}^{2}}({{a}^{2}}+{{b}^{2}})-{{a}^{2}}{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}}\] done
clear
C)
\[2\frac{\sqrt{{{r}^{2}}({{a}^{2}}+{{b}^{2}})-{{a}^{2}}{{b}^{2}}}}{{{a}^{2}}+{{b}^{2}}}\] done
clear
D)
None of these done
clear
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question_answer8)
Middle point of the chord of the circle \[{{x}^{2}}+{{y}^{2}}=25\] intercepted on the line \[x-2y=2\]is
A)
\[\left( \frac{3}{5},\frac{4}{5} \right)\] done
clear
B)
\[(-2,-2)\] done
clear
C)
\[\left( \frac{2}{5},-\frac{4}{5} \right)\] done
clear
D)
\[\left( \frac{8}{3},\frac{1}{3} \right)\] done
clear
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question_answer9)
If the line \[x-2y=k\]cuts off a chord of length 2 from the circle \[{{x}^{2}}+{{y}^{2}}=3\], then k =
A)
0 done
clear
B)
\[\pm 1\] done
clear
C)
\[\pm \sqrt{10}\] done
clear
D)
None of these done
clear
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question_answer10)
From the origin chords are drawn to the circle\[{{(x-1)}^{2}}+{{y}^{2}}=1\]. The equation of the locus of the middle points of these chords is [IIT 1985; EAMCET 1991]
A)
\[{{x}^{2}}+{{y}^{2}}-3x=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-3y=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-x=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-y=0\] done
clear
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question_answer11)
The polars drawn from (-1, 2) to the circles \[{{S}_{1}}\equiv {{x}^{2}}+{{y}^{2}}+6y+7=0\]and \[{{S}_{2}}\equiv {{x}^{2}}+{{y}^{2}}+6x+1=0\], are [RPET 2002]
A)
Parallel done
clear
B)
Equal done
clear
C)
Perpendicular done
clear
D)
Intersect at a point done
clear
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question_answer12)
The equation of the diameter of the circle \[{{x}^{2}}+{{y}^{2}}+2x-4y-11=0\]which bisects the chords intercepted on the line \[2x-y+3=0\]is
A)
\[x+y-7=0\] done
clear
B)
\[2x-y-5=0\] done
clear
C)
\[x+2y-3=0\] done
clear
D)
None of these done
clear
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question_answer13)
If the lengths of the chords intercepted by the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy=0\]from the co-ordinate axes be 10 and 24 respectively, then the radius of the circle is
A)
17 done
clear
B)
9 done
clear
C)
14 done
clear
D)
13 done
clear
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question_answer14)
The equation of the common chord of the circles \[{{(x-a)}^{2}}+{{(y-b)}^{2}}={{c}^{2}}\]and \[{{(x-b)}^{2}}+{{(y-a)}^{2}}={{c}^{2}}\] is
A)
\[x-y=0\] done
clear
B)
\[x+y=0\] done
clear
C)
\[x+y={{a}^{2}}+{{b}^{2}}\] done
clear
D)
\[x-y={{a}^{2}}-{{b}^{2}}\] done
clear
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question_answer15)
The length of common chord of the circles \[{{(x-a)}^{2}}+{{y}^{2}}={{a}^{2}}\]and \[{{x}^{2}}+{{(y-b)}^{2}}={{b}^{2}}\]is [MP PET 1989]
A)
\[2\sqrt{{{a}^{2}}+{{b}^{2}}}\] done
clear
B)
\[\frac{ab}{\sqrt{{{a}^{2}}+{{b}^{2}}}}\] done
clear
C)
\[\frac{2ab}{\sqrt{{{a}^{2}}+{{b}^{2}}}}\] done
clear
D)
None of these done
clear
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question_answer16)
The co-ordinates of pole of line \[lx+my+n=0\]with respect to circles \[{{x}^{2}}+{{y}^{2}}=1\], is [RPET 1987]
A)
\[\left( \frac{l}{n},\frac{m}{n} \right)\] done
clear
B)
\[\left( -\frac{l}{n},-\frac{m}{n} \right)\] done
clear
C)
\[\left( \frac{l}{n},-\frac{m}{n} \right)\] done
clear
D)
\[\left( -\frac{l}{n},\frac{m}{n} \right)\] done
clear
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question_answer17)
The length of common chord of the circles \[{{x}^{2}}+{{y}^{2}}=12\]and \[{{x}^{2}}+{{y}^{2}}-4x+3y-2=0\], is [RPET 1990, 99]
A)
\[4\sqrt{2}\] done
clear
B)
\[5\sqrt{2}\] done
clear
C)
\[2\sqrt{2}\] done
clear
D)
\[6\sqrt{2}\] done
clear
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question_answer18)
The length of the common chord of the circles \[{{(x-a)}^{2}}+{{(y-b)}^{2}}={{c}^{2}}\]and \[{{(x-b)}^{2}}+{{(y-a)}^{2}}={{c}^{2}}\], is
A)
\[\sqrt{4{{c}^{2}}-2{{(a-b)}^{2}}}\] done
clear
B)
\[\sqrt{4{{c}^{2}}+2{{(a-b)}^{2}}}\] done
clear
C)
\[\sqrt{4{{c}^{2}}-2{{(a+b)}^{2}}}\] done
clear
D)
\[\sqrt{4{{c}^{2}}+2{{(a+b)}^{2}}}\] done
clear
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question_answer19)
The locus of the middle points of chords of the circle \[{{x}^{2}}+{{y}^{2}}-2x-6y-10=0\] which passes through the origin, is [Roorkee 1989]
A)
\[{{x}^{2}}+{{y}^{2}}+x+3y=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-x+3y=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+x-3y=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-x-3y=0\] done
clear
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question_answer20)
The distance between the chords of contact of the tangents to the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\]from the origin and the point \[(g,f)\]is
A)
\[\frac{1}{2}\left( \frac{{{g}^{2}}+{{f}^{2}}-c}{\sqrt{{{g}^{2}}+{{f}^{2}}}} \right)\] done
clear
B)
\[\left( \frac{{{g}^{2}}+{{f}^{2}}-c}{\sqrt{{{g}^{2}}+{{f}^{2}}}} \right)\] done
clear
C)
\[\frac{1}{2}\left( \frac{{{g}^{2}}+{{f}^{2}}-c}{{{g}^{2}}+{{f}^{2}}} \right)\] done
clear
D)
None of these done
clear
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question_answer21)
The pole of the straight line \[x+2y=1\]with respect to the circle \[{{x}^{2}}+{{y}^{2}}=5\]is [RPET 2000, 01]
A)
(5, 5) done
clear
B)
(5, 10) done
clear
C)
(10, 5) done
clear
D)
(10, 10) done
clear
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question_answer22)
A line \[lx+my+n=0\]meets the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]at the points P and Q. The tangents drawn at the points P and Q meet at R, then the coordinates of R is
A)
\[\left( \frac{{{a}^{2}}l}{n},\frac{{{a}^{2}}m}{n} \right)\] done
clear
B)
\[\left( \frac{-{{a}^{2}}l}{n},\frac{-{{a}^{2}}m}{n} \right)\] done
clear
C)
\[\left( \frac{{{a}^{2}}n}{l},\frac{{{a}^{2}}n}{m} \right)\] done
clear
D)
None of these done
clear
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question_answer23)
Polar of origin (0, 0) with respect to the circle \[{{x}^{2}}+{{y}^{2}}+2\lambda x+2\mu y+c=0\] touches the circle \[{{x}^{2}}+{{y}^{2}}={{r}^{2}}\], if [RPET 1992]
A)
\[c=r({{\lambda }^{2}}+{{\mu }^{2}})\] done
clear
B)
\[r=c\,({{\lambda }^{2}}+{{\mu }^{2}})\] done
clear
C)
\[{{c}^{2}}={{r}^{2}}({{\lambda }^{2}}+{{\mu }^{2}})\] done
clear
D)
\[{{r}^{2}}={{c}^{2}}({{\lambda }^{2}}+{{\mu }^{2}})\] done
clear
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question_answer24)
Tangents AB and AC are drawn from the point \[A(0,\,1)\]to the circle \[{{x}^{2}}+{{y}^{2}}-2x+4y+1=0\]. Equation of the circle through A, B and C is
A)
\[{{x}^{2}}+{{y}^{2}}+x+y-2=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-x+y-2=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+x-y-2=0\] done
clear
D)
None of these done
clear
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question_answer25)
Length of the common chord of the circles \[{{x}^{2}}+{{y}^{2}}+5x+7y+9=0\]and \[{{x}^{2}}+{{y}^{2}}+7x+5y+9=0\]is [Kurukshetra CEE 1996]
A)
9 done
clear
B)
8 done
clear
C)
7 done
clear
D)
6 done
clear
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question_answer26)
The locus of midpoint of the chords of the circle \[{{x}^{2}}+{{y}^{2}}-2x-2y-2=0\]which makes an angle of \[120{}^\circ \] at the centre is [MNR 1994]
A)
\[{{x}^{2}}+{{y}^{2}}-2x-2y+1=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+x+y-1=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-2x-2y-1=0\] done
clear
D)
None of these done
clear
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question_answer27)
If the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]cuts off a chord of length 2b from the line \[y=mx+c\], then
A)
\[(1-{{m}^{2}})({{a}^{2}}+{{b}^{2}})={{c}^{2}}\] done
clear
B)
\[(1+{{m}^{2}})({{a}^{2}}-{{b}^{2}})={{c}^{2}}\] done
clear
C)
\[(1-{{m}^{2}})({{a}^{2}}-{{b}^{2}})={{c}^{2}}\] done
clear
D)
None of these done
clear
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question_answer28)
The pole of the straight line \[9x+y-28=0\]with respect to circle \[2{{x}^{2}}+2{{y}^{2}}-3x+5y-7=0\], is [RPET 1990, 99; MNR 1984; UPSEAT 2000]
A)
(3, 1) done
clear
B)
(1, 3) done
clear
C)
(3, -1) done
clear
D)
(-3, 1) done
clear
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question_answer29)
If polar of a circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]with respect to \[(x',y')\] is \[Ax+By+C=0\], then its pole will be [RPET 1995]
A)
\[\left( \frac{{{a}^{2}}A}{-C},\frac{{{a}^{2}}B}{-C} \right)\] done
clear
B)
\[\left( \frac{{{a}^{2}}A}{C},\frac{{{a}^{2}}B}{C} \right)\] done
clear
C)
\[\left( \frac{{{a}^{2}}C}{A},\frac{{{a}^{2}}C}{B} \right)\] done
clear
D)
\[\left( \frac{{{a}^{2}}C}{-A},\frac{{{a}^{2}}C}{-B} \right)\] done
clear
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question_answer30)
The polar of the point (5, ?1/2) w.r.t circle \[{{(x-2)}^{2}}+{{y}^{2}}=4\]is [RPET 1996]
A)
\[5x-10y+2=0\] done
clear
B)
\[6x-y-20=0\] done
clear
C)
\[10x-y-10=0\] done
clear
D)
\[x-10y-2=0\] done
clear
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question_answer31)
The pole of the line \[2x+3y=4\]w.r.t circle \[{{x}^{2}}+{{y}^{2}}=64\] is [RPET 1996]
A)
(32, 48) done
clear
B)
(48, 32) done
clear
C)
(- 32, 48) done
clear
D)
(48, -32) done
clear
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question_answer32)
The length of the common chord of the circles \[{{x}^{2}}+{{y}^{2}}+2x+3y+1=0\]and \[{{x}^{2}}+{{y}^{2}}+4x+3y+2=0\]is [MP PET 2000]
A)
\[9/2\] done
clear
B)
\[2\sqrt{2}\] done
clear
C)
\[3\sqrt{2}\] done
clear
D)
\[3/2\] done
clear
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question_answer33)
The length of the chord joining the points in which the straight line \[\frac{x}{3}+\frac{y}{4}=1\]cuts the circle \[{{x}^{2}}+{{y}^{2}}=\frac{169}{25}\]is [Orissa JEE 2003]
A)
1 done
clear
B)
2 done
clear
C)
4 done
clear
D)
8 done
clear
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question_answer34)
Which of the following is a point on the common chord of the circles \[{{x}^{2}}+{{y}^{2}}+2x-3y+6=0\]and \[{{x}^{2}}+{{y}^{2}}+x-8y-13=0\] Karnataka CET 2003]
A)
(1, -2) done
clear
B)
(1, 4) done
clear
C)
(1, 2) done
clear
D)
(1, -4) done
clear
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question_answer35)
If the circle \[{{x}^{2}}+{{y}^{2}}=4\]bisects the circumference of the circle \[{{x}^{2}}+{{y}^{2}}-2x+6y+a=0\], then a equals [RPET 1999]
A)
4 done
clear
B)
-4 done
clear
C)
16 done
clear
D)
-16 done
clear
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question_answer36)
The equation of polar of the point (1, 2)with respect to the circle \[{{x}^{2}}+{{y}^{2}}=7\], is [RPET 1983, 84; MNR 1973]
A)
\[x-2y-7=0\] done
clear
B)
\[x+2y-7=0\] done
clear
C)
\[x-2y=0\] done
clear
D)
\[x+2y=0\] done
clear
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question_answer37)
The equation of the chord of contact, if the tangents are drawn from the point (5, ?3) to the circle \[{{x}^{2}}+{{y}^{2}}=10\], is
A)
\[5x-3y=10\] done
clear
B)
\[5x+3y=10\] done
clear
C)
\[3x+5y=10\] done
clear
D)
\[3x-5y=10\] done
clear
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question_answer38)
A line through (0,0) cuts the circle \[{{x}^{2}}+{{y}^{2}}-2ax=0\] at A and B, then locus of the centre of the circle drawn on AB as a diameter is [RPET 2002]
A)
\[{{x}^{2}}+{{y}^{2}}-2ay=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+ay=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+ax=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-ax=0\] done
clear
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question_answer39)
The radius of the circle, having centre at (2,1) whose one of the chord is a diameter of the circle \[{{x}^{2}}+{{y}^{2}}-2x-6y+6=0\] is [IIT Screening 2004]
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
\[\sqrt{3}\] done
clear
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question_answer40)
The intercept on the line \[y=x\] by the circle \[{{x}^{2}}+{{y}^{2}}-2x=0\] is AB, equation of the circle on AB as a diameter is [AIEEE 2004]
A)
\[{{x}^{2}}+{{y}^{2}}+x-y=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-x+y=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+x+y=\]0 done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-x-y=0\] done
clear
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question_answer41)
The equation of the circle having as a diameter, the chord \[x-y-1=0\] of the circle \[2{{x}^{2}}+2{{y}^{2}}-2x-6y-25=0\], is
A)
\[{{x}^{2}}+{{y}^{2}}-3x-y-\frac{29}{2}=0\] done
clear
B)
\[2{{x}^{2}}+2{{y}^{2}}+2x-5y-\frac{29}{2}=0\] done
clear
C)
\[2{{x}^{2}}+2{{y}^{2}}-6x-2y-21=0\] done
clear
D)
None of these done
clear
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