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Conic Section

119861 The number of common tangents to the circles \(x^2+y^2=4\) and \(x^2+y^2-6 x-8 y-24=0\) is

1 3
2 4
3 2
4 1
BCECE-2012
Conic Section

119862 The circle \(S_1\) with centre \(C_1\left(a_1, b_1\right)\) and radius \(r_1\) touches externally the circle \(S_2\) with centre \(\mathbf{C}_2\left(\mathbf{a}_2, \mathrm{~b}_2\right)\) and radius \(\mathbf{r}_2\). If the tangent at their common point passes through the origin, then

1 \(\left(a_1^2+a_2^2\right)+\left(b_1^2+b_2^2\right)=r_1^2+r_2^2\)
2 \(\left(a_1^2-a_2^2\right)+\left(b_1^2-b_2^2\right)=r_1^2-r_2^2\)
3 \(\left(\mathrm{a}_1^2-\mathrm{b}_2\right)^2+\left(\mathrm{a}_2^2+\mathrm{b}_2^2\right)=\mathrm{r}_1^2+\mathrm{r}_2^2\)
4 \(\left(\mathrm{a}_1^2-\mathrm{b}_1^2\right)+\left(\mathrm{a}_1^2+\mathrm{b}_2^2\right)=\mathrm{r}_1^2+\mathrm{r}_2^2\)
BCECE-2011
Conic Section

119863 The equation of a circle of radius 5 which lies within the circle \(x^2+y^2+14 x+10 y-26=0\) and touches it at the point \((-1,3)\) is

1 \(x^2+y^2+8 x+2 y+8=0\)
2 \(x^2+y^2+8 x+2 y-8=0\)
3 \(x^2+y^2+8 x+2 y-14=0\)
4 None of the above
BCECE-2010
Conic Section

119864 The number of common tangents to two circles \(x^2+y^2=4\) and \(x^2+y^2-8 x+12=0\) is

1 1
2 2
3 3
4 4
CG PET- 2015
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Conic Section

119861 The number of common tangents to the circles \(x^2+y^2=4\) and \(x^2+y^2-6 x-8 y-24=0\) is

1 3
2 4
3 2
4 1
BCECE-2012
Conic Section

119862 The circle \(S_1\) with centre \(C_1\left(a_1, b_1\right)\) and radius \(r_1\) touches externally the circle \(S_2\) with centre \(\mathbf{C}_2\left(\mathbf{a}_2, \mathrm{~b}_2\right)\) and radius \(\mathbf{r}_2\). If the tangent at their common point passes through the origin, then

1 \(\left(a_1^2+a_2^2\right)+\left(b_1^2+b_2^2\right)=r_1^2+r_2^2\)
2 \(\left(a_1^2-a_2^2\right)+\left(b_1^2-b_2^2\right)=r_1^2-r_2^2\)
3 \(\left(\mathrm{a}_1^2-\mathrm{b}_2\right)^2+\left(\mathrm{a}_2^2+\mathrm{b}_2^2\right)=\mathrm{r}_1^2+\mathrm{r}_2^2\)
4 \(\left(\mathrm{a}_1^2-\mathrm{b}_1^2\right)+\left(\mathrm{a}_1^2+\mathrm{b}_2^2\right)=\mathrm{r}_1^2+\mathrm{r}_2^2\)
BCECE-2011
Conic Section

119863 The equation of a circle of radius 5 which lies within the circle \(x^2+y^2+14 x+10 y-26=0\) and touches it at the point \((-1,3)\) is

1 \(x^2+y^2+8 x+2 y+8=0\)
2 \(x^2+y^2+8 x+2 y-8=0\)
3 \(x^2+y^2+8 x+2 y-14=0\)
4 None of the above
BCECE-2010
Conic Section

119864 The number of common tangents to two circles \(x^2+y^2=4\) and \(x^2+y^2-8 x+12=0\) is

1 1
2 2
3 3
4 4
CG PET- 2015
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Conic Section

119861 The number of common tangents to the circles \(x^2+y^2=4\) and \(x^2+y^2-6 x-8 y-24=0\) is

1 3
2 4
3 2
4 1
BCECE-2012
Conic Section

119862 The circle \(S_1\) with centre \(C_1\left(a_1, b_1\right)\) and radius \(r_1\) touches externally the circle \(S_2\) with centre \(\mathbf{C}_2\left(\mathbf{a}_2, \mathrm{~b}_2\right)\) and radius \(\mathbf{r}_2\). If the tangent at their common point passes through the origin, then

1 \(\left(a_1^2+a_2^2\right)+\left(b_1^2+b_2^2\right)=r_1^2+r_2^2\)
2 \(\left(a_1^2-a_2^2\right)+\left(b_1^2-b_2^2\right)=r_1^2-r_2^2\)
3 \(\left(\mathrm{a}_1^2-\mathrm{b}_2\right)^2+\left(\mathrm{a}_2^2+\mathrm{b}_2^2\right)=\mathrm{r}_1^2+\mathrm{r}_2^2\)
4 \(\left(\mathrm{a}_1^2-\mathrm{b}_1^2\right)+\left(\mathrm{a}_1^2+\mathrm{b}_2^2\right)=\mathrm{r}_1^2+\mathrm{r}_2^2\)
BCECE-2011
Conic Section

119863 The equation of a circle of radius 5 which lies within the circle \(x^2+y^2+14 x+10 y-26=0\) and touches it at the point \((-1,3)\) is

1 \(x^2+y^2+8 x+2 y+8=0\)
2 \(x^2+y^2+8 x+2 y-8=0\)
3 \(x^2+y^2+8 x+2 y-14=0\)
4 None of the above
BCECE-2010
Conic Section

119864 The number of common tangents to two circles \(x^2+y^2=4\) and \(x^2+y^2-8 x+12=0\) is

1 1
2 2
3 3
4 4
CG PET- 2015
For More Updates join with Us
Conic Section

119861 The number of common tangents to the circles \(x^2+y^2=4\) and \(x^2+y^2-6 x-8 y-24=0\) is

1 3
2 4
3 2
4 1
BCECE-2012
Conic Section

119862 The circle \(S_1\) with centre \(C_1\left(a_1, b_1\right)\) and radius \(r_1\) touches externally the circle \(S_2\) with centre \(\mathbf{C}_2\left(\mathbf{a}_2, \mathrm{~b}_2\right)\) and radius \(\mathbf{r}_2\). If the tangent at their common point passes through the origin, then

1 \(\left(a_1^2+a_2^2\right)+\left(b_1^2+b_2^2\right)=r_1^2+r_2^2\)
2 \(\left(a_1^2-a_2^2\right)+\left(b_1^2-b_2^2\right)=r_1^2-r_2^2\)
3 \(\left(\mathrm{a}_1^2-\mathrm{b}_2\right)^2+\left(\mathrm{a}_2^2+\mathrm{b}_2^2\right)=\mathrm{r}_1^2+\mathrm{r}_2^2\)
4 \(\left(\mathrm{a}_1^2-\mathrm{b}_1^2\right)+\left(\mathrm{a}_1^2+\mathrm{b}_2^2\right)=\mathrm{r}_1^2+\mathrm{r}_2^2\)
BCECE-2011
Conic Section

119863 The equation of a circle of radius 5 which lies within the circle \(x^2+y^2+14 x+10 y-26=0\) and touches it at the point \((-1,3)\) is

1 \(x^2+y^2+8 x+2 y+8=0\)
2 \(x^2+y^2+8 x+2 y-8=0\)
3 \(x^2+y^2+8 x+2 y-14=0\)
4 None of the above
BCECE-2010
Conic Section

119864 The number of common tangents to two circles \(x^2+y^2=4\) and \(x^2+y^2-8 x+12=0\) is

1 1
2 2
3 3
4 4
CG PET- 2015