Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 60

HARD

JEE Advanced

IMPORTANT

Earn 100

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 $x^{2} + y^{2} - 2 a x = 0$ passes, through the point

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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>Entrances Gallery>Q 61

If the lines joining the origin to the intersection of the line

y = m x + 2

and the circle

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

are at right angles, then

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 62

The total number of common tangents of

x^{2} + y^{2} - 6 x - 8 y + 9 = 0

and

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

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 63

The centre of a circle which cuts

x^{2} + y^{2} + 6 x - 1 = 0, x^{2} + y^{2} - 3 y + 2 = 0

and

x^{2} + y^{2} + x + y - 3 = 0

orthogonally is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 64

The line segment joining the points

(4, 7)

and

(- 2, - 1)

is a diameter of a circle. If the circle intersects

x

-axis at

A

and

B

, then

A B

is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 65

The distance of the midpoint of the line joining two points

(4, 0)

and

(0, 4)

from the centre of the circle

x^{2} + y^{2} = 16

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 66

The equation of family of circles with centre at

(h, k)

touching

x

-axis, is given by

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 67

The straight line

x + y - 1 = 0

meets the circle

x^{2} + y^{2} - 6 x - 8 y = 0

at

A

and

B

. Then, the equation of the circle of which

A B

is a diameter, is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 68

The equation of normal of

x^{2} + y^{2} - 2 x + 4 y - 5 = 0

at

(2, 1)

is