Tangent and Normal to Circle
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Conic Section

119856 The number of common tangents to the circles \(x^2+y^2-6 x-14 y+48=0\) and \(x^2+y^2-6 x=0\) is

1 1
2 2
3 0
4 4
VITEEE-2016
Conic Section

119857 The line \(2 x+\sqrt{6} y=2\) is a tangent to the curve \(x^2-2 y^2=4\). The point of contact is

1 \((4,-\sqrt{6})\)
2 \((7,-2 \sqrt{6})\)
3 \((2,3)\)
4 \((\sqrt{6,1})\)
VITEEE-2013
Conic Section

119858 If \(O A\) and \(O B\) are the tangents to the circle \(x^2+\) \(y^2-6 x-8 y+21=0\) drawn from the origin \(O\), then \(A B\) is equal to

1 11
2 \(\frac{4}{5} \sqrt{21}\)
3 \(\sqrt{\frac{17}{3}}\)
4 None of these
UPSEE-2015
Conic Section

119859 Tangent are drawn from the points on the line \(x-y-5=0\) to \(x^2+4 y^2=4\), then all the chords of contact pass through a fixed point, whose coordinate are

1 \(\left(\frac{4}{5},-\frac{1}{5}\right)\)
2 \(\left(\frac{4}{5}, \frac{1}{5}\right)\)
3 \(\left(-\frac{4}{5}, \frac{1}{5}\right)\)
4 None of these
UPSEE-2013
Conic Section

119860 The locus of a point which moves so that the ratio of the length of the tangents to the circles \(x^2+y^2+4 x+3=0\) and \(x^2+y^2-6 x+5=0\) is 2 : 3 is

1 \(5 \mathrm{x}^2+5 \mathrm{y}^2-60 \mathrm{x}+7=0\)
2 \(5 \mathrm{x}^2+5 \mathrm{y}^2+60 \mathrm{x}+7=0\)
3 \(5 \mathrm{x}^2+5 \mathrm{y}^2+60 \mathrm{x}+12=0\)
4 None of the above
BCECE-2014
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Conic Section

119856 The number of common tangents to the circles \(x^2+y^2-6 x-14 y+48=0\) and \(x^2+y^2-6 x=0\) is

1 1
2 2
3 0
4 4
VITEEE-2016
Conic Section

119857 The line \(2 x+\sqrt{6} y=2\) is a tangent to the curve \(x^2-2 y^2=4\). The point of contact is

1 \((4,-\sqrt{6})\)
2 \((7,-2 \sqrt{6})\)
3 \((2,3)\)
4 \((\sqrt{6,1})\)
VITEEE-2013
Conic Section

119858 If \(O A\) and \(O B\) are the tangents to the circle \(x^2+\) \(y^2-6 x-8 y+21=0\) drawn from the origin \(O\), then \(A B\) is equal to

1 11
2 \(\frac{4}{5} \sqrt{21}\)
3 \(\sqrt{\frac{17}{3}}\)
4 None of these
UPSEE-2015
Conic Section

119859 Tangent are drawn from the points on the line \(x-y-5=0\) to \(x^2+4 y^2=4\), then all the chords of contact pass through a fixed point, whose coordinate are

1 \(\left(\frac{4}{5},-\frac{1}{5}\right)\)
2 \(\left(\frac{4}{5}, \frac{1}{5}\right)\)
3 \(\left(-\frac{4}{5}, \frac{1}{5}\right)\)
4 None of these
UPSEE-2013
Conic Section

119860 The locus of a point which moves so that the ratio of the length of the tangents to the circles \(x^2+y^2+4 x+3=0\) and \(x^2+y^2-6 x+5=0\) is 2 : 3 is

1 \(5 \mathrm{x}^2+5 \mathrm{y}^2-60 \mathrm{x}+7=0\)
2 \(5 \mathrm{x}^2+5 \mathrm{y}^2+60 \mathrm{x}+7=0\)
3 \(5 \mathrm{x}^2+5 \mathrm{y}^2+60 \mathrm{x}+12=0\)
4 None of the above
BCECE-2014
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Conic Section

119856 The number of common tangents to the circles \(x^2+y^2-6 x-14 y+48=0\) and \(x^2+y^2-6 x=0\) is

1 1
2 2
3 0
4 4
VITEEE-2016
Conic Section

119857 The line \(2 x+\sqrt{6} y=2\) is a tangent to the curve \(x^2-2 y^2=4\). The point of contact is

1 \((4,-\sqrt{6})\)
2 \((7,-2 \sqrt{6})\)
3 \((2,3)\)
4 \((\sqrt{6,1})\)
VITEEE-2013
Conic Section

119858 If \(O A\) and \(O B\) are the tangents to the circle \(x^2+\) \(y^2-6 x-8 y+21=0\) drawn from the origin \(O\), then \(A B\) is equal to

1 11
2 \(\frac{4}{5} \sqrt{21}\)
3 \(\sqrt{\frac{17}{3}}\)
4 None of these
UPSEE-2015
Conic Section

119859 Tangent are drawn from the points on the line \(x-y-5=0\) to \(x^2+4 y^2=4\), then all the chords of contact pass through a fixed point, whose coordinate are

1 \(\left(\frac{4}{5},-\frac{1}{5}\right)\)
2 \(\left(\frac{4}{5}, \frac{1}{5}\right)\)
3 \(\left(-\frac{4}{5}, \frac{1}{5}\right)\)
4 None of these
UPSEE-2013
Conic Section

119860 The locus of a point which moves so that the ratio of the length of the tangents to the circles \(x^2+y^2+4 x+3=0\) and \(x^2+y^2-6 x+5=0\) is 2 : 3 is

1 \(5 \mathrm{x}^2+5 \mathrm{y}^2-60 \mathrm{x}+7=0\)
2 \(5 \mathrm{x}^2+5 \mathrm{y}^2+60 \mathrm{x}+7=0\)
3 \(5 \mathrm{x}^2+5 \mathrm{y}^2+60 \mathrm{x}+12=0\)
4 None of the above
BCECE-2014
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Conic Section

119856 The number of common tangents to the circles \(x^2+y^2-6 x-14 y+48=0\) and \(x^2+y^2-6 x=0\) is

1 1
2 2
3 0
4 4
VITEEE-2016
Conic Section

119857 The line \(2 x+\sqrt{6} y=2\) is a tangent to the curve \(x^2-2 y^2=4\). The point of contact is

1 \((4,-\sqrt{6})\)
2 \((7,-2 \sqrt{6})\)
3 \((2,3)\)
4 \((\sqrt{6,1})\)
VITEEE-2013
Conic Section

119858 If \(O A\) and \(O B\) are the tangents to the circle \(x^2+\) \(y^2-6 x-8 y+21=0\) drawn from the origin \(O\), then \(A B\) is equal to

1 11
2 \(\frac{4}{5} \sqrt{21}\)
3 \(\sqrt{\frac{17}{3}}\)
4 None of these
UPSEE-2015
Conic Section

119859 Tangent are drawn from the points on the line \(x-y-5=0\) to \(x^2+4 y^2=4\), then all the chords of contact pass through a fixed point, whose coordinate are

1 \(\left(\frac{4}{5},-\frac{1}{5}\right)\)
2 \(\left(\frac{4}{5}, \frac{1}{5}\right)\)
3 \(\left(-\frac{4}{5}, \frac{1}{5}\right)\)
4 None of these
UPSEE-2013
Conic Section

119860 The locus of a point which moves so that the ratio of the length of the tangents to the circles \(x^2+y^2+4 x+3=0\) and \(x^2+y^2-6 x+5=0\) is 2 : 3 is

1 \(5 \mathrm{x}^2+5 \mathrm{y}^2-60 \mathrm{x}+7=0\)
2 \(5 \mathrm{x}^2+5 \mathrm{y}^2+60 \mathrm{x}+7=0\)
3 \(5 \mathrm{x}^2+5 \mathrm{y}^2+60 \mathrm{x}+12=0\)
4 None of the above
BCECE-2014
Join With Us for More Updates
Conic Section

119856 The number of common tangents to the circles \(x^2+y^2-6 x-14 y+48=0\) and \(x^2+y^2-6 x=0\) is

1 1
2 2
3 0
4 4
VITEEE-2016
Conic Section

119857 The line \(2 x+\sqrt{6} y=2\) is a tangent to the curve \(x^2-2 y^2=4\). The point of contact is

1 \((4,-\sqrt{6})\)
2 \((7,-2 \sqrt{6})\)
3 \((2,3)\)
4 \((\sqrt{6,1})\)
VITEEE-2013
Conic Section

119858 If \(O A\) and \(O B\) are the tangents to the circle \(x^2+\) \(y^2-6 x-8 y+21=0\) drawn from the origin \(O\), then \(A B\) is equal to

1 11
2 \(\frac{4}{5} \sqrt{21}\)
3 \(\sqrt{\frac{17}{3}}\)
4 None of these
UPSEE-2015
Conic Section

119859 Tangent are drawn from the points on the line \(x-y-5=0\) to \(x^2+4 y^2=4\), then all the chords of contact pass through a fixed point, whose coordinate are

1 \(\left(\frac{4}{5},-\frac{1}{5}\right)\)
2 \(\left(\frac{4}{5}, \frac{1}{5}\right)\)
3 \(\left(-\frac{4}{5}, \frac{1}{5}\right)\)
4 None of these
UPSEE-2013
Conic Section

119860 The locus of a point which moves so that the ratio of the length of the tangents to the circles \(x^2+y^2+4 x+3=0\) and \(x^2+y^2-6 x+5=0\) is 2 : 3 is

1 \(5 \mathrm{x}^2+5 \mathrm{y}^2-60 \mathrm{x}+7=0\)
2 \(5 \mathrm{x}^2+5 \mathrm{y}^2+60 \mathrm{x}+7=0\)
3 \(5 \mathrm{x}^2+5 \mathrm{y}^2+60 \mathrm{x}+12=0\)
4 None of the above
BCECE-2014