A) \[(1+\sqrt{2},\ -2)\] done clear
B) \[(1-\sqrt{2},\ -2)\] done clear
C) \[(1,\ -2+\sqrt{2})\] done clear
D) None of these done clear
View Solution play_arrowA) 3 done clear
B) - 5 done clear
C) - 1 done clear
D) 5 done clear
View Solution play_arrowA) An ellipse done clear
B) A circle done clear
C) A parabola done clear
D) A hyperbola done clear
View Solution play_arrowA) 2 done clear
B) 4 done clear
C) \[\frac{5}{2}\] done clear
D) \[\frac{7}{2}\] done clear
View Solution play_arrowquestion_answer5) If the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] touches x-axis, then
A) \[g=f\] done clear
B) \[{{g}^{2}}=c\] done clear
C) \[{{f}^{2}}=c\] done clear
D) \[{{g}^{2}}+{{f}^{2}}=c\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-2ax-2ay+{{a}^{2}}=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}+ax+ay-{{a}^{2}}=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+2ax+2ay-{{a}^{2}}=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-ax-ay+{{a}^{2}}=0\] done clear
View Solution play_arrowA) \[5\pi \] done clear
B) \[10\pi \] done clear
C) \[25\pi \] done clear
D) None of these done clear
View Solution play_arrowA) Same done clear
B) Collinear done clear
C) Non-collinear done clear
D) None of these done clear
View Solution play_arrowA) \[(a,\ b)\] done clear
B) \[(b,\ a)\] done clear
C) \[\left( \frac{a}{2},\ \frac{b}{2} \right)\] done clear
D) \[\left( \frac{b}{2},\ -\frac{a}{2} \right)\] done clear
View Solution play_arrowA) \[5{{x}^{2}}+5{{y}^{2}}-10x+30y+49=0\] done clear
B) \[5{{x}^{2}}+5{{y}^{2}}+10x-30y+49=0\] done clear
C) \[5{{x}^{2}}+5{{y}^{2}}-10x+30y-49=0\] done clear
D) None of these done clear
View Solution play_arrowquestion_answer11) The circle \[{{x}^{2}}+{{y}^{2}}+4x-4y+4=0\] touches [MP PET 1988]
A) x-axis done clear
B) y-axis done clear
C) x-axis and y-axis done clear
D) None of these done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}+2{{x}_{1}}(x+y)+x_{1}^{2}=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-2{{x}_{1}}(x+y)+x_{1}^{2}=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}=x_{1}^{2}+y_{1}^{2}\] done clear
D) \[{{x}^{2}}+{{y}^{2}}+2x{{x}_{1}}+2y{{y}_{1}}=0\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-18x-16y-120=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-18x-16y+120=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+18x+16y-120=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}+18x-16y+120=0\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}+2x-2y=62\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-2x+2y=47\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+2x-2y=47\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-2x+2y=62\] done clear
View Solution play_arrowA) 3 done clear
B) 4 done clear
C) 5 done clear
D) 6 done clear
View Solution play_arrowA) One done clear
B) Two done clear
C) Four done clear
D) Infinite done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-2x+4y+1=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-2x-4y+1=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+2x+4y+1=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}+4x+2y+4=0\] done clear
View Solution play_arrowA) \[x+y=a+b\] done clear
B) \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}+{{b}^{2}}\] done clear
C) \[{{x}^{2}}-{{y}^{2}}={{a}^{2}}-{{b}^{2}}\] done clear
D) \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}-{{b}^{2}}\] done clear
View Solution play_arrowA) 3/2 done clear
B) 3/4 done clear
C) 1/10 done clear
D) 1/20 done clear
View Solution play_arrowA) 347 done clear
B) 4 done clear
C) \[-\,4\] done clear
D) 49 done clear
View Solution play_arrowA) \[\left( \frac{{{x}_{1}}+{{y}_{1}}}{2},\ \frac{{{x}_{2}}+{{y}_{2}}}{2} \right)\] done clear
B) \[\left( \frac{{{x}_{1}}-{{y}_{1}}}{2},\ \frac{{{x}_{2}}-{{y}_{2}}}{2} \right)\] done clear
C) \[\left( \frac{{{x}_{1}}+{{x}_{2}}}{2},\ \frac{{{y}_{1}}+{{y}_{2}}}{2} \right)\] done clear
D) \[\left( \frac{{{x}_{1}}-{{x}_{2}}}{2},\ \frac{{{y}_{1}}-{{y}_{2}}}{2} \right)\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-6x+8y=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}=25\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-3x+4y+5=0\] done clear
D) None of these done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-2x-2y+1=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-2x-2y-1=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-2x-2y=0\] done clear
D) None of these done clear
View Solution play_arrowquestion_answer24) The number of circles touching the line \[y-x=0\] and the y-axis is
A) Zero done clear
B) One done clear
C) Two done clear
D) Infinite done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-2x+3y-3=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}+2x-3y-5=0\] done clear
C) \[2{{x}^{2}}+2{{y}^{2}}-2x+5y-8=0\] done clear
D) None of these done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}+3x+3y+8=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-3x-3y-8=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-3x+3y+8=0\] done clear
D) None of these done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-4x+4y-4=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-4x+4y+4=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+4x+4y+4=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-4x-4y-4=0\] done clear
View Solution play_arrowA) (0, 0) done clear
B) (1, 1) done clear
C) (1, 2) done clear
D) (2, 1) done clear
View Solution play_arrowA) 3, 1 done clear
B) 2, 2 done clear
C) 3, 2 done clear
D) 3, 4 done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}+6x+8y+1=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-6x-8y=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+3x+4y=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-3x-4y=0\] done clear
View Solution play_arrowquestion_answer31) Circle \[{{x}^{2}}+{{y}^{2}}+6y=0\]touches
A) y-axis at the origin done clear
B) x-axis at the origin done clear
C) x-axis at the point (3, 0) done clear
D) The line \[y+3=0\] done clear
View Solution play_arrowA) \[{{g}^{2}}+{{f}^{2}}=c\] done clear
B) \[{{g}^{2}}+{{f}^{2}}>c\] done clear
C) \[{{g}^{2}}+{{f}^{2}}+c=0\] done clear
D) None of these done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-2x+4y-20=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-2x-4y-20=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+2x-4y-20=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}+2x+4y-20=0\] done clear
View Solution play_arrowA) Circle passes through the point \[(-3,\ 4)\] done clear
B) Circle touches x-axis done clear
C) Circle touches y-axis done clear
D) None of these done clear
View Solution play_arrowA) \[{{x}^{2}}-4x+{{y}^{2}}+4y+4=0\] done clear
B) \[{{x}^{2}}-4x+{{y}^{2}}-4y+4=0\] done clear
C) \[{{x}^{2}}+4x+{{y}^{2}}+4y+4=0\] done clear
D) \[{{x}^{2}}+4x+{{y}^{2}}-4y+4=0\] done clear
View Solution play_arrowA) Line is a tangent to the circle done clear
B) Line is a chord of the circle done clear
C) Line is a diameter of the circle done clear
D) None of these done clear
View Solution play_arrowA) \[{{x}^{2}}+2by={{b}^{2}}+{{a}^{2}}\] done clear
B) \[{{x}^{2}}-2by={{b}^{2}}+{{a}^{2}}\] done clear
C) \[{{x}^{2}}+2by={{a}^{2}}-{{b}^{2}}\] done clear
D) \[{{x}^{2}}-2by={{b}^{2}}-{{a}^{2}}\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}+4x+4y-5=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-4x-4y-5=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-4x=13\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-4x-4y+5=0\] done clear
View Solution play_arrowA) A straight line done clear
B) A circle done clear
C) An ellipse done clear
D) A hyperbola done clear
View Solution play_arrowquestion_answer40) Radius of circle \[(x-5)(x-1)+(y-7)(y-4)=0\] is
A) 3 done clear
B) 4 done clear
C) 5/2 done clear
D) 7/2 done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}+4x-10y+25=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-4x-10y+25=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-4x-10y+16=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-14y+8=0\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-2x+4y+3=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-2x+4y-3=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+2x-4y-3=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}+2x-4y+3=0\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}+8x+10y+59=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}+8x+10y-59=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-4x-6y+87=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-4x-6y-87=0\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}+ax+by=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-ax+by=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-ax-by=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}+ax-by=0\] done clear
View Solution play_arrowA) \[a=b=0\] and \[c=0\] done clear
B) \[f=g\] and \[h=0\] done clear
C) \[a=b\ne 0\] and \[h=0\] done clear
D) \[f=g\] and \[c=0\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-2x-2y+1=0,\ {{x}^{2}}+{{y}^{2}}-10x-10y+25=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-2x-2y-1=0,\ {{x}^{2}}+{{y}^{2}}-10x-10y-25=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+2x+2y+1=0,\ {{x}^{2}}+{{y}^{2}}+10x+10y+25=0\] done clear
D) None of these done clear
View Solution play_arrowA) \[3x-4y=0\] done clear
B) \[4x-3y=9\] done clear
C) \[x+y=7\] done clear
D) \[x-y=1\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-6x+12y-15=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-6x+12y+15=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-6x+12y+45=0\] done clear
D) None of these done clear
View Solution play_arrowA) \[g=f=r\] done clear
B) \[g=f=c=r\] done clear
C) \[g=f=\sqrt{c}=r\] done clear
D) \[g=f\] and \[{{c}^{2}}=r\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}+4x=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-8y=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}\pm 8x=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}+8y=0\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-5x=0\] done clear
B) \[2{{x}^{2}}+2{{y}^{2}}-5x=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+5x=0\] done clear
D) None of these done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-2x+2y=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}+2x-2y=0\] 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_arrowA) Centre lies on x-axis done clear
B) Centre lies on y-axis done clear
C) Centre is at origin done clear
D) Circle passes through origin done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}+4x-21=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}+4x+21=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-4x-21=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}+5x-21=0\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-6x-5y+9=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}+6x+5y-9=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-6x+5y-9=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}+6x-5y+9=0\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-16x+4y-32=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}+16x+4y-32=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+16x+4y+32=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}+16x-4y+32=0\] done clear
View Solution play_arrowquestion_answer57) The number of circles touching the lines \[x=0\], \[y=a\] and \[y=b\] is
A) One done clear
B) Two done clear
C) Four done clear
D) Infinite done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-ax-by=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}+ax-by=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-ax+by=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}+ax+by=0\] done clear
View Solution play_arrowA) \[\left( \frac{1}{4},\ 0 \right)\] and \[\frac{1}{4}\] done clear
B) \[\left( -\frac{1}{2},\ 0 \right)\] and \[\frac{1}{2}\] done clear
C) \[\left( \frac{1}{2},\ 0 \right)\] and \[\frac{1}{2}\] done clear
D) \[\left( 0,\ -\frac{1}{4} \right)\] and \[\frac{1}{4}\] done clear
View Solution play_arrowquestion_answer60) Centre of the circle \[{{(x-3)}^{2}}+{{(y-4)}^{2}}=5\] is [MP PET 1988]
A) (3, 4) done clear
B) \[(-3,\ -4)\] done clear
C) (4, 3) done clear
D) \[(-4,\ -3)\] done clear
View Solution play_arrowquestion_answer61) The equation of the circle touching \[x=0,y=0\] and \[x=4\] is [UPSEAT 2004]
A) \[{{x}^{2}}+{{y}^{2}}-4x-4y+16=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-8x-8y+16=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+4x+4y+4=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-4x-4y+4=0\] done clear
View Solution play_arrowquestion_answer62) The equation \[{{x}^{2}}+{{y}^{2}}=0\] denotes [MP PET 1984]
A) A point done clear
B) A circle done clear
C) x-axis done clear
D) y-axis done clear
View Solution play_arrowA) \[a=0,\ b=0,\ c=2\] done clear
B) \[a=1,\ b=0,\ c=0\] done clear
C) \[a=2,\ b=2,\ c=0\] done clear
D) \[a=2,\ b=0,\ c=0\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}=1\] done clear
B) \[{{x}^{2}}+{{y}^{2}}=\sqrt{2}\] done clear
C) \[{{x}^{2}}+{{y}^{2}}=4\] done clear
D) \[{{x}^{2}}+{{y}^{2}}=-4\] done clear
View Solution play_arrowA) (3, -3) done clear
B) (0, 0) done clear
C) (-3, 0) done clear
D) (6, -6) done clear
View Solution play_arrowA) \[{{(x-2)}^{2}}+{{(y-3)}^{2}}=8\] done clear
B) \[{{(x-2)}^{2}}+{{(y-3)}^{2}}=3\] done clear
C) \[{{(x+2)}^{2}}+{{(y+3)}^{2}}=2\sqrt{2}\] done clear
D) \[{{(x-2)}^{2}}+{{(y-3)}^{2}}=2\sqrt{2}\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-ax-by=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}+ax+by=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-ax+by=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}+ax-by=0\] done clear
View Solution play_arrowA) ? 4 done clear
B) 4 done clear
C) 0 done clear
D) 1 done clear
View Solution play_arrowA) \[f=2a,\ g=0,\ c=3{{a}^{2}}\] done clear
B) \[f=0,\ g=a,\ c=3{{a}^{2}}\] done clear
C) \[f=0,\ g=-2a,\ c=3{{a}^{2}}\] done clear
D) None of these done clear
View Solution play_arrowA) \[x+3y=0\] done clear
B) \[x-3y=0\] done clear
C) \[3x+y=0\] done clear
D) \[3x-y=0\] done clear
View Solution play_arrowA) 3 done clear
B) 2 done clear
C) 5 done clear
D) 8 done clear
View Solution play_arrowA) Straight line done clear
B) Circle done clear
C) Parabola done clear
D) A pair of straight lines done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-4y=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}+4x=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-4y=12\] done clear
D) \[{{x}^{2}}+{{y}^{2}}+4x=12\] done clear
View Solution play_arrowquestion_answer74) The equation \[{{x}^{2}}+{{y}^{2}}+4x+6y+13=0\] represents [Roorkee 1990]
A) Circle done clear
B) Pair of coincident straight lines done clear
C) Pair of concurrent straight lines done clear
D) Point done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}+8x-6y+9=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}+8x+6y-11=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+8x+6y-9=0\] done clear
D) None of these done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-4x-6y-9=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-4x-6y+9=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-4x-6y+3=0\] done clear
D) None of these done clear
View Solution play_arrowquestion_answer77) Locus of the centre of the circle touching both the co-ordinates axes is
A) \[{{x}^{2}}+{{y}^{2}}=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}=\]a non-zero constant done clear
C) \[{{x}^{2}}-{{y}^{2}}=0\] done clear
D) \[{{x}^{2}}-{{y}^{2}}=\]a non-zero constant done clear
View Solution play_arrowA) \[m(m+n)\] done clear
B) \[m+n\] done clear
C) \[n(m+n)\] done clear
D) \[\frac{1}{2}(m+n)\] done clear
View Solution play_arrowA) 1 done clear
B) 3 done clear
C) \[2\sqrt{3}\] done clear
D) \[\sqrt{10}\] done clear
View Solution play_arrowA) \[{{l}_{1}}{{l}_{2}}={{m}_{1}}{{m}_{2}}\] done clear
B) \[{{l}_{1}}{{m}_{1}}={{l}_{2}}{{m}_{2}}\] done clear
C) \[{{l}_{1}}{{l}_{2}}+{{m}_{1}}{{m}_{2}}=0\] done clear
D) \[{{l}_{1}}{{m}_{2}}={{l}_{2}}{{m}_{1}}\] done clear
View Solution play_arrowA) Incentre of the triangle done clear
B) Centroid of the triangle done clear
C) Orthocentre of the triangle done clear
D) None of these done clear
View Solution play_arrowA) A circle passing through origin done clear
B) A circle of radius 2a done clear
C) A concentric circle of radius \[a\sqrt{2}\] done clear
D) None of these done clear
View Solution play_arrowA) \[x=1\] done clear
B) \[x+y=6\] done clear
C) \[x+y=2a\] done clear
D) \[x=0\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}+4x-2y-35=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-4x+2y+35=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+4x+2y+35=0\] done clear
D) None of these done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}+4x+4y-5=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-4x-4y-5=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-4x=13\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-4x-4y+5=0\] done clear
View Solution play_arrowA) \[{{x}^{2}}-6x-10y+14=0\] done clear
B) \[{{x}^{2}}-10x-6y+14=0\] done clear
C) \[{{y}^{2}}-6x-10y+14=0\] done clear
D) \[{{y}^{2}}-10x-6y+14=0\] done clear
View Solution play_arrowquestion_answer87) The area of a circle whose centre is (h, k) and radius a is [MP PET 1994]
A) \[\pi ({{h}^{2}}+{{k}^{2}}-{{a}^{2}})\] done clear
B) \[\pi {{a}^{2}}hk\] done clear
C) \[\pi {{a}^{2}}\] done clear
D) None of these done clear
View Solution play_arrowA) 3/4 done clear
B) 1 done clear
C) 4/3 done clear
D) 12 done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-8x-6y+16=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}+8x+6y+16=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-8x-6y-16=0\] done clear
D) None of these done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}+8x+2y+51=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}+8x-2y-51=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+8x+2y-51=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-8x-2y-51=0\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-3x-12y+2=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-3x+12y+2=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+3x+12y+2=0\] done clear
D) None of these done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}+3x-6y+5=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}+3x-6y-31=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+3x-6y+\frac{29}{4}=0\] done clear
D) None of these done clear
View Solution play_arrowA) \[\frac{\pi }{2}\] done clear
B) \[2\pi \] done clear
C) \[\pi \] done clear
D) \[\frac{\pi }{4}\] done clear
View Solution play_arrowA) \[S+\lambda P=0\] done clear
B) \[S-\lambda P=0\] done clear
C) \[\lambda S+P=0\] done clear
D) \[P-\lambda S=0\] done clear
E) All of these done clear
View Solution play_arrowA) (5, 3) done clear
B) (6, 2) done clear
C) (1, -8) done clear
D) (11, 2) done clear
View Solution play_arrowquestion_answer96) For \[a{{x}^{2}}+2hxy+3{{y}^{2}}+4x+8y-6=0\] to represent a circle, one must have
A) \[a=3,\ h=0\] done clear
B) \[a=1,\ h=0\] done clear
C) \[a=h=3\] done clear
D) \[a=h=0\] done clear
View Solution play_arrowA) \[{{(\alpha +\beta )}^{2}}-{{r}^{2}}\] done clear
B) \[{{(\alpha +\beta )}^{2}}-{{r}^{2}}\] done clear
C) \[{{(\alpha -\beta )}^{2}}+{{r}^{2}}\] done clear
D) None of these done clear
View Solution play_arrowA) (1, ?3) done clear
B) (?1, 3) done clear
C) (1, 3) done clear
D) None of these done clear
View Solution play_arrowA) \[x=1,\ y=4\] done clear
B) \[x=4,\ y=1\] done clear
C) \[x=8,\ y=2\] done clear
D) None of these done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}+9x+2fy+14=0\] done clear
B) \[3{{x}^{2}}+3{{y}^{2}}+27x-2fy+42=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-9x+2fy+14=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-2fy-9y+14=0\] done clear
View Solution play_arrowA) \[{{(x-2)}^{2}}+{{(y-8)}^{2}}=25\] done clear
B) \[5{{x}^{2}}+5{{y}^{2}}-12x-24y+31=0\] done clear
C) Both (a) and (b) done clear
D) None of these done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}+5x+5y+25=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-10x-10y+25=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-5x-5y+25=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}+10x+10y+25=0\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-2x-2y+1=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-x-y=0\] done clear
C) \[2{{x}^{2}}+2{{y}^{2}}-3x-3y+1=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-3x-3y+2=0\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}+2x+3y-5=0\] done clear
B) \[6({{x}^{2}}+{{y}^{2}})-5\text{ }(3x+2y)=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-2x-3y+5=0\] done clear
D) \[6({{x}^{2}}+{{y}^{2}})+5\text{ }(3x+2y)=0\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-\alpha x-\beta y=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}+2\alpha x+2\beta y=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-2\alpha x-2\beta y=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}+\alpha x+\beta y=0\] done clear
View Solution play_arrowquestion_answer106) The equation \[2{{x}^{2}}+2{{y}^{2}}+4x+8y+15=0\] represents [Roorkee 1999]
A) A pair of straight lines done clear
B) A circle done clear
C) An ellipse done clear
D) None of these done clear
View Solution play_arrowA) \[5\text{ }({{x}^{2}}+{{y}^{2}})-3x-8y=200\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-4x-8y=200\] done clear
C) \[5\text{ }({{x}^{2}}+{{y}^{2}})-4x=200\] done clear
D) \[{{x}^{2}}+{{y}^{2}}=40\] done clear
View Solution play_arrowquestion_answer108) The area of the curve \[{{x}^{2}}+{{y}^{2}}=2ax\]is [MP PET 1996]
A) \[\pi {{a}^{2}}\] done clear
B) \[2\pi {{a}^{2}}\] done clear
C) \[4\pi {{a}^{2}}\] done clear
D) \[\frac{1}{2}\pi {{a}^{2}}\] done clear
View Solution play_arrowquestion_answer109) Radius of the circle \[(x-1)(x-3)+(y-2)(y-4)\] \[=0\] is
A) 2 done clear
B) \[\sqrt{2}\] done clear
C) 3 done clear
D) \[2\sqrt{2}\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-2x+2y-47=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-2x+2y+47=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+2x-2y-47=0\] done clear
D) None of these done clear
View Solution play_arrowA) x-axis only done clear
B) y- axis only done clear
C) Both x and y- axis done clear
D) Does not touch any axis done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}+2x-4y+6=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-2x-4y+3=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-2x+4y+8=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-2x-4y+8=0\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}+2x-4y-4=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}+4x-2y-4=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-3x-4y=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-4x-2y=0\] done clear
View Solution play_arrowA) \[{{(x-5)}^{2}}+{{(y+5)}^{2}}=25\] done clear
B) \[{{(x+4)}^{2}}+{{(y+4)}^{2}}=25\] done clear
C) \[{{(x+6)}^{2}}+{{(y+6)}^{2}}=25\] done clear
D) \[{{(x+5)}^{2}}+{{(y+5)}^{2}}=25\] done clear
View Solution play_arrowA) \[(2,\,0),(-3,\,0)\] done clear
B) \[(3,\,0),(4,\,0)\] done clear
C) \[(1,\,0),(-1,\,0)\] done clear
D) \[(1,\,0),(2,\,0)\] done clear
View Solution play_arrowA) A circle of radius g done clear
B) A circle of radius f done clear
C) A circle of diameter \[\sqrt{c}\] done clear
D) A circle of radius 0 done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}+4x+6y+12=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-4x+6y+12=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-4x+6y-12=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-4x-6y-12=0\] done clear
View Solution play_arrowA) A circle done clear
B) An Ellipse done clear
C) A hyperbola done clear
D) A parabola done clear
View Solution play_arrowA) \[2\,\pi \,R\] done clear
B) \[\pi \,R\] done clear
C) \[4R\] done clear
D) \[\pi \,{{R}^{2}}\] done clear
View Solution play_arrowA) (4, 7) done clear
B) (7, 4) done clear
C) (9, 4) done clear
D) (4, 9) done clear
View Solution play_arrowA) 2 done clear
B) 1 done clear
C) 4 done clear
D) 5 done clear
View Solution play_arrowA) - 2 done clear
B) 2 done clear
C) 1 done clear
D) 0 done clear
View Solution play_arrowA) (?1, 0), \[(6,\sqrt{35})\] done clear
B) \[(3,-\sqrt{26}),(-3,\sqrt{26})\] done clear
C) \[(6,-\sqrt{35})\], \[(3,-\sqrt{26})\] done clear
D) \[(0,\,-1),(-6,-\sqrt{35})\] done clear
View Solution play_arrowA) 4 done clear
B) 6 done clear
C) 20 done clear
D) \[\sqrt{20}\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}+2x-2y-23=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-2x-2y-23=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}+2x-2y-23=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-2x+2y-23=0\] done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-2gx-2gy+{{g}^{2}}=0\], where \[g=\frac{2}{(\cos \alpha +\sin \alpha +1)}\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-2gx-2gy+{{g}^{2}}=0\], where \[g=\frac{2}{(\cos \alpha +\sin \alpha -1)}\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-2gx+2gy+{{g}^{2}}=0\], where \[g=\frac{2}{(\cos \alpha -\sin \alpha +1)}\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-2gx+2gy+{{g}^{2}}=0\] where \[g=\frac{2}{(\cos \alpha +\sin \alpha +1)}\] done clear
E) All of these done clear
View Solution play_arrowquestion_answer127) If a circle and a square have the same perimeter, then [Pb. CET 2001]
A) Their area are equal done clear
B) Area of circle is larger done clear
C) Area of square is larger done clear
D) None of these done clear
View Solution play_arrowA) 2 done clear
B) 4 done clear
C) 6 done clear
D) 8 done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}-4x-2y+5=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-4x-2y-5=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-4x-2y+4=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-4x-2y-4=0\] done clear
View Solution play_arrowA) (3, 3) done clear
B) \[(2,\,\,-1)\] done clear
C) \[(-2,\,\,1)\] done clear
D) \[(-1,\,\,2)\] done clear
View Solution play_arrowA) \[\sqrt{26}\] done clear
B) \[\sqrt{13}\] done clear
C) \[\sqrt{23}\] done clear
D) 0 done clear
View Solution play_arrowA) \[(-1,-2)\] done clear
B) \[(1,\,\,2)\] done clear
C) \[(1,-2)\] done clear
D) \[(-1,2)\] done clear
View Solution play_arrowA) \[\,k\in I\] done clear
B) \[k<0\] done clear
C) \[0<k<1\] done clear
D) For two values of k done clear
View Solution play_arrowA) \[x+y=1\] done clear
B) \[2(x-y)=5\] done clear
C) \[2x+2y=5\] done clear
D) None of these done clear
View Solution play_arrowA) \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] done clear
B) \[{{x}^{2}}-{{y}^{2}}={{a}^{2}}\] done clear
C) \[x+y={{a}^{2}}\] done clear
D) \[{{x}^{2}}-{{y}^{2}}=4{{a}^{2}}\] done clear
E) \[{{x}^{2}}+{{y}^{2}}=4{{a}^{2}}\] done clear
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