Different Cases of Two Circles
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Conic Section

119989 For the given circles \(x^2+y^2-6 x-2 y+1=0\) and \(x^2+y^2+2 x-8 y+13=0\), which of the following is true?

1 One circle lies inside the other
2 One circle lies completely outside the other
3 Two circle intersect in two points
4 They touch each other externally
BCECE-2016
Conic Section

119990 The circles \(x^2+y^2-5 x+6 y+15=0\) and \(x^2+y^2-2 x+6 y+6=0\) touch each other

1 internally
2 externally
3 Do not say anything
4 None of these
BCECE-2014
Conic Section

119991 If two circles \((x-1)^2+(y-3)^2=r^2\) and \(x^2+y^2-8 x+2 y+8=0\) intersect in two distinct points, then

1 \(2\lt \mathrm{r}\lt 8\)
2 \(\mathrm{r}\lt 2\)
3 \(\mathrm{r}=2\)
4 \(\mathrm{r}>2\)
AP EAMCET-20.04.2019
Conic Section

119992 The locus of the point of intersection of the tangents at the extremities of a chord of the circle \(x^2+y^2=a^2\) which touches the circle \(\mathbf{x}^2+\mathbf{y}^2-\mathbf{2 a x}=0\) passes through the point

1 \((\mathrm{a} / 2,0)\)
2 \((0, a / 2)\)
3 \((\mathrm{a}, 0)\)
4 \((0,0)\)
AMU-2011
Conic Section

119993 The angle between circles \(x^2+y^2+2 x+4 y+1\) \(=0\) and \(x^2+y^2-2 x+6 y-3=0\) is:

1 \(\cos ^{-1}\left(\frac{3}{\sqrt{13}}\right)\)
2 \(\cos ^{-1}\left(\frac{3}{\sqrt{31}}\right)\)
3 \(\cos ^{-1}\left(\sqrt{\frac{3}{31}}\right)\)
4 \(2 \cos ^{-1}\left(\frac{3}{\sqrt{13}}\right)\)
APEAPCET-20.08.2021
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Conic Section

119989 For the given circles \(x^2+y^2-6 x-2 y+1=0\) and \(x^2+y^2+2 x-8 y+13=0\), which of the following is true?

1 One circle lies inside the other
2 One circle lies completely outside the other
3 Two circle intersect in two points
4 They touch each other externally
BCECE-2016
Conic Section

119990 The circles \(x^2+y^2-5 x+6 y+15=0\) and \(x^2+y^2-2 x+6 y+6=0\) touch each other

1 internally
2 externally
3 Do not say anything
4 None of these
BCECE-2014
Conic Section

119991 If two circles \((x-1)^2+(y-3)^2=r^2\) and \(x^2+y^2-8 x+2 y+8=0\) intersect in two distinct points, then

1 \(2\lt \mathrm{r}\lt 8\)
2 \(\mathrm{r}\lt 2\)
3 \(\mathrm{r}=2\)
4 \(\mathrm{r}>2\)
AP EAMCET-20.04.2019
Conic Section

119992 The locus of the point of intersection of the tangents at the extremities of a chord of the circle \(x^2+y^2=a^2\) which touches the circle \(\mathbf{x}^2+\mathbf{y}^2-\mathbf{2 a x}=0\) passes through the point

1 \((\mathrm{a} / 2,0)\)
2 \((0, a / 2)\)
3 \((\mathrm{a}, 0)\)
4 \((0,0)\)
AMU-2011
Conic Section

119993 The angle between circles \(x^2+y^2+2 x+4 y+1\) \(=0\) and \(x^2+y^2-2 x+6 y-3=0\) is:

1 \(\cos ^{-1}\left(\frac{3}{\sqrt{13}}\right)\)
2 \(\cos ^{-1}\left(\frac{3}{\sqrt{31}}\right)\)
3 \(\cos ^{-1}\left(\sqrt{\frac{3}{31}}\right)\)
4 \(2 \cos ^{-1}\left(\frac{3}{\sqrt{13}}\right)\)
APEAPCET-20.08.2021
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Conic Section

119989 For the given circles \(x^2+y^2-6 x-2 y+1=0\) and \(x^2+y^2+2 x-8 y+13=0\), which of the following is true?

1 One circle lies inside the other
2 One circle lies completely outside the other
3 Two circle intersect in two points
4 They touch each other externally
BCECE-2016
Conic Section

119990 The circles \(x^2+y^2-5 x+6 y+15=0\) and \(x^2+y^2-2 x+6 y+6=0\) touch each other

1 internally
2 externally
3 Do not say anything
4 None of these
BCECE-2014
Conic Section

119991 If two circles \((x-1)^2+(y-3)^2=r^2\) and \(x^2+y^2-8 x+2 y+8=0\) intersect in two distinct points, then

1 \(2\lt \mathrm{r}\lt 8\)
2 \(\mathrm{r}\lt 2\)
3 \(\mathrm{r}=2\)
4 \(\mathrm{r}>2\)
AP EAMCET-20.04.2019
Conic Section

119992 The locus of the point of intersection of the tangents at the extremities of a chord of the circle \(x^2+y^2=a^2\) which touches the circle \(\mathbf{x}^2+\mathbf{y}^2-\mathbf{2 a x}=0\) passes through the point

1 \((\mathrm{a} / 2,0)\)
2 \((0, a / 2)\)
3 \((\mathrm{a}, 0)\)
4 \((0,0)\)
AMU-2011
Conic Section

119993 The angle between circles \(x^2+y^2+2 x+4 y+1\) \(=0\) and \(x^2+y^2-2 x+6 y-3=0\) is:

1 \(\cos ^{-1}\left(\frac{3}{\sqrt{13}}\right)\)
2 \(\cos ^{-1}\left(\frac{3}{\sqrt{31}}\right)\)
3 \(\cos ^{-1}\left(\sqrt{\frac{3}{31}}\right)\)
4 \(2 \cos ^{-1}\left(\frac{3}{\sqrt{13}}\right)\)
APEAPCET-20.08.2021
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Conic Section

119989 For the given circles \(x^2+y^2-6 x-2 y+1=0\) and \(x^2+y^2+2 x-8 y+13=0\), which of the following is true?

1 One circle lies inside the other
2 One circle lies completely outside the other
3 Two circle intersect in two points
4 They touch each other externally
BCECE-2016
Conic Section

119990 The circles \(x^2+y^2-5 x+6 y+15=0\) and \(x^2+y^2-2 x+6 y+6=0\) touch each other

1 internally
2 externally
3 Do not say anything
4 None of these
BCECE-2014
Conic Section

119991 If two circles \((x-1)^2+(y-3)^2=r^2\) and \(x^2+y^2-8 x+2 y+8=0\) intersect in two distinct points, then

1 \(2\lt \mathrm{r}\lt 8\)
2 \(\mathrm{r}\lt 2\)
3 \(\mathrm{r}=2\)
4 \(\mathrm{r}>2\)
AP EAMCET-20.04.2019
Conic Section

119992 The locus of the point of intersection of the tangents at the extremities of a chord of the circle \(x^2+y^2=a^2\) which touches the circle \(\mathbf{x}^2+\mathbf{y}^2-\mathbf{2 a x}=0\) passes through the point

1 \((\mathrm{a} / 2,0)\)
2 \((0, a / 2)\)
3 \((\mathrm{a}, 0)\)
4 \((0,0)\)
AMU-2011
Conic Section

119993 The angle between circles \(x^2+y^2+2 x+4 y+1\) \(=0\) and \(x^2+y^2-2 x+6 y-3=0\) is:

1 \(\cos ^{-1}\left(\frac{3}{\sqrt{13}}\right)\)
2 \(\cos ^{-1}\left(\frac{3}{\sqrt{31}}\right)\)
3 \(\cos ^{-1}\left(\sqrt{\frac{3}{31}}\right)\)
4 \(2 \cos ^{-1}\left(\frac{3}{\sqrt{13}}\right)\)
APEAPCET-20.08.2021
Join With Us for More Updates
Conic Section

119989 For the given circles \(x^2+y^2-6 x-2 y+1=0\) and \(x^2+y^2+2 x-8 y+13=0\), which of the following is true?

1 One circle lies inside the other
2 One circle lies completely outside the other
3 Two circle intersect in two points
4 They touch each other externally
BCECE-2016
Conic Section

119990 The circles \(x^2+y^2-5 x+6 y+15=0\) and \(x^2+y^2-2 x+6 y+6=0\) touch each other

1 internally
2 externally
3 Do not say anything
4 None of these
BCECE-2014
Conic Section

119991 If two circles \((x-1)^2+(y-3)^2=r^2\) and \(x^2+y^2-8 x+2 y+8=0\) intersect in two distinct points, then

1 \(2\lt \mathrm{r}\lt 8\)
2 \(\mathrm{r}\lt 2\)
3 \(\mathrm{r}=2\)
4 \(\mathrm{r}>2\)
AP EAMCET-20.04.2019
Conic Section

119992 The locus of the point of intersection of the tangents at the extremities of a chord of the circle \(x^2+y^2=a^2\) which touches the circle \(\mathbf{x}^2+\mathbf{y}^2-\mathbf{2 a x}=0\) passes through the point

1 \((\mathrm{a} / 2,0)\)
2 \((0, a / 2)\)
3 \((\mathrm{a}, 0)\)
4 \((0,0)\)
AMU-2011
Conic Section

119993 The angle between circles \(x^2+y^2+2 x+4 y+1\) \(=0\) and \(x^2+y^2-2 x+6 y-3=0\) is:

1 \(\cos ^{-1}\left(\frac{3}{\sqrt{13}}\right)\)
2 \(\cos ^{-1}\left(\frac{3}{\sqrt{31}}\right)\)
3 \(\cos ^{-1}\left(\sqrt{\frac{3}{31}}\right)\)
4 \(2 \cos ^{-1}\left(\frac{3}{\sqrt{13}}\right)\)
APEAPCET-20.08.2021