Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Target Exercises>Q 93

HARD

JEE Advanced

IMPORTANT

Earn 100

One possible equation of the chord of the circle $x^{2} + y^{2} = 100$ that passes through $(1, 7)$ and subtends an angle $\frac{2 π}{3}$ at the origin, is

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Important Questions on Circle

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Target Exercises>Q 94

Tangents are drawn to

x^{2} + y^{2} = 1

from any arbitrary point

P

on the circle

C_{1} : x^{2} + y^{2} - 4 = 0 .

These tangents meets the circle

C_{1}

again in

A

and

B

. Locus of point of intersection of tangents drawn to

C_{1}

at

A

and

B

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Target Exercises>Q 95

If the circle

x^{2} + y^{2} + 2 a_{1} x + c = 0

lies completely inside the circle

x^{2} + y^{2} + 2 a_{2} x + c = 0,

then

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Target Exercises>Q 96

If the angle between tangents drawn to

x^{2} + y^{2} - 2 x - 4 y + 1 = 0

at the points, where it is cut by the line

y = 2 x + c

is

\frac{π}{2}

. Then,

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Target Exercises>Q 97

A circle touches the lines

y = \frac{x}{\sqrt{3}}, y = x \sqrt{3}

and has unit radius. If the centre of this circle lies in the first quadrant, then possible equation of this circle is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Target Exercises>Q 98

The equation of the circle which passes through the point

(2 a, 0)

and whose radical axis with respect to the circle

x^{2} + y^{2} = a^{2}

is the line

x = \frac{a}{2}

, is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Target Exercises>Q 99

The equation of the system of coaxial circles that are tangent at

(\sqrt{2}, 4)

to the locus of the point of intersection of two mutually perpendicular tangents to the circle

x^{2} + y^{2} = 9

, is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Target Exercises>Q 100

The equation of the circle passing through the origin and cutting the circles

x^{2} + y^{2} - 4 x + 6 y + 10 = 0

and

x^{2} + y^{2} + 12 y + 6 = 0

at right angles, is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Target Exercises>Q 101

^{The equation of the circle which cuts orthogonally the circle $x^{2} + y^{2} - 6 x + 4 y - 3 = 0$ , passes through $(3, 0)$ and touches $y$ -axis, is}