Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Work Book Exercise 13.2>Q 2

HARD

JEE Advanced

IMPORTANT

Earn 100

The locus of the point of intersection of perpendicular tangents to the circles $x^{2} + y^{2} = a^{2}$ and $x^{2} + y^{2} = b^{2}$ is

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Important Questions on Circle

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Work Book Exercise 13.2>Q 3

If the line

y = m x

does not intersect the circle

(x + 10)^{2} + (y + 10)^{2} = 180

, then

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Work Book Exercise 13.2>Q 4

If the circle

x^{2} + y^{2} + 4 x + 22 y + c = 0

bisects the circumference of the circle

x^{2} + y^{2} - 2 x + 8 y - d = 0

, then

c + d

is equal to

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Work Book Exercise 13.2>Q 5

If

A B

is the intercept of the tangent of a circle

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

between the coordinate axes, then the locus of the vertex

P

of the rectangle

O A P B

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Work Book Exercise 13.2>Q 6

The area of the triangle formed by the tangent at the point

(a, b)

to the circle

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

and the coordinate axes is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Work Book Exercise 13.2>Q 7

If two circles

a (x^{2} + y^{2}) + b x + c y = 0

and

A (x^{2} + y^{2}) + B x + C y = 0

touch each other, then

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Work Book Exercise 13.2>Q 8

The circles which can be drawn, to pass through

(1, 0)

and

(3, 0)

and touch the

Y

-axis intersect at an angle

θ,

then

\cos θ

is equal to

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Work Book Exercise 13.2>Q 9

The locus of the point of intersection of the tangents to the circle

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

at points whose parametric angles differ by

\frac{π}{3},

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Work Book Exercise 13.2>Q 10

If $α, β$ are the roots of the equation $35 x^{2} - 24 x - 35 = 0,$ then the parametric equations $x = α + a \cos θ, y = β + a \sin θ$ can represent a family of

( $a$ is arbitrary constant)