MEDIUM

JEE Main

IMPORTANT

Earn 100

The points of intersection of the line $a x + b y = 0$ , $(a \neq b)$ and the circle $x^{2} + y^{2} - 2 x = 0$ are $A (α, 0)$ and $B (1, β)$ . The image of the circle with $A B$ as a diameter in the line $x + y + 2 = 0$ is :

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Important Questions on Circle

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 25 January 2023 Shift 2>Q 96

Points

P (- 3, 2), Q (9, 10)

and

R (α, 4)

lie on a circle

C

with

P R

as its diameter. The tangents to

C

at the points

Q

and

R

intersect at the point

S

. If

S

lies on the line

2 x - k y = 1

, then

k

is equal to _____ .

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 29 January 2023 Shift 1>Q 97

Let the tangents at the points

A (4, - 11)

and

B (8, - 5)

on the circle

x^{2} + y^{2} - 3 x + 10 y - 15 = 0

, intersect at the point

C

. Then the radius of the circle, whose centre is

C

and the line joining

A

and

B

is its tangent, is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 29 January 2023 Shift 2>Q 98

A circle with centre

(2, 3)

and radius

4

intersects the line

x + y = 3

at the points

P

and

Q

. If the tangents at

P

and

Q

intersect at the point

S (α, β)

, then

4 α - 7 β

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 30 January 2023 Shift 1>Q 99

Let

y = x + 2, 4 y = 3 x + 6

and

3 y = 4 x + 1

be three tangent lines to the circle

(x - h)^{2} + (y - k)^{2} = r^{2}

. Then

h + k

is equal to :

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 30 January 2023 Shift 2>Q 100

Let

P (a_{1}, b_{1})

and

Q (a_{2}, b_{2})

be two distinct points on a circle with center

C (\sqrt{2}, \sqrt{3})

. Let

O

be the origin and

O C

be perpendicular to both

C P

and

C Q

. If the area of the triangle

O C P

\frac{\sqrt{35}}{2}

, then

a_{1}^{2} + a_{2}^{2} + b_{1}^{2} + b_{2}^{2}

is equal to __________

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 31 January 2023 Shift 1>Q 101

Let a circle

C_{1}

be obtained on rolling the circle

x^{2} + y^{2} - 4 x - 6 y + 11 = 0

upwards

4

units on the tangent

T

to it at the point

(3, 2)

. Let

C_{2}

be the image of

C_{1}

T

. Let

A

and

B

be the centers of circles

C_{1}

and

C_{2}

respectively, and

M

and

N

be respectively the feet of perpendiculars drawn from

A

and

B

on the

x

-axis. Then the area of the trapezium AMNB is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 31 January 2023 Shift 2>Q 102

The set of all values of

a^{2}

for which the line

x + y = 0

bisects two distinct chords drawn from a point

P (\frac{1 + a}{2}, \frac{1 - a}{2})

on the circle

2 x^{2} + 2 y^{2} - (1 + a) x - (1 - a) y = 0

, is equal to :

The points of intersection of the line ax + by=0, (a≠b) and the circle x2+y2-2x=0 are A(α,0) and B(1,β). The image of the circle with AB as a diameter in the line x+y+2=0 is :

Important Questions on Circle

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The points of intersection of the line $a x + b y = 0$ , $(a \neq b)$ and the circle $x^{2} + y^{2} - 2 x = 0$ are $A (α, 0)$ and $B (1, β)$ . The image of the circle with $A B$ as a diameter in the line $x + y + 2 = 0$ is :