Tangents drawn from point of intersection A of circles x 2 + y 2 = 4 and x - 3 2 + y - 3 2 = 4 cut the line joining their centers at B and C , then triangle B A C is a/an

isosceles triangle and ∠ A B C = π / 6

MEDIUM

JEE Main

IMPORTANT

Earn 100

The line $y = m x$ intersects the circle $x^{2} + y^{2} - 2 x - 2 y = 0$ and $x^{2} + y^{2} + 6 x - 8 y = 0$ at points $A$ and $B$ (points being other than origin). The range of $m$ such that origin divides $A B$ internally is

70.37% studentsanswered this correctly

Important Questions on Circles

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 4 - Circles>DPP>Q 9

C_{1} : x^{2} + y^{2} = {(3 + 2 \sqrt{2})}^{2}

be a circle.

P A

and

P B

are pair of tangents on

C_{1}

, where

P

is any point on the director circle of

C_{1}

, then the radius of the smallest circle which touches

C_{1}

externally and also the two tangents

P A

and

P B

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 4 - Circles>DPP>Q 10

From points on the straight line

3 x - 4 y + 12 = 0,

tangents are drawn to the circle

x^{2} + y^{2} = 4 .

Then the chord of contact passes through a fixed point. The slope of the chord of the circle having this fixed point as its midpoint is

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 4 - Circles>DPP>Q 11

If the tangent at

(1, 2)

to the circle

C_{1} : x^{2} + y^{2} = 5

intersects the circle

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

A

and

B

and tangents at

A

and

B

to the second circle meet at point

C

, then the coordinates of

C

are given by

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 4 - Circles>DPP>Q 1

$A B$ is a line segment of length $48 cm$ and $C$ is its mid-point. If three semicircles are drawn at $A B, A C$ and $C B$ using as diameters, then the radius of the circle inscribed in the region enclosed by three semicircles is

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 4 - Circles>DPP>Q 2

Consider circles:

$C_{1} : x^{2} + y^{2} + 2 x - 2 y + p = 0$

$C_{2} : x^{2} + y^{2} - 2 x + 2 y - p = 0$

$C_{3} : x^{2} + y^{2} = p^{2}$

Statement-I: If the circle $C_{3}$ intersects $C_{1}$ orthogonally then $C_{2}$ does not represent a circle.

Statement-II: If the circle $C_{3}$ intersects $C_{2}$ orthogonally then $C_{2}$ and $C_{3}$ have equal radii.

Then which of the following is true?

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 4 - Circles>DPP>Q 3

Tangents drawn from point of intersection

A

of circles

x^{2} + y^{2} = 4

and

{(x - \sqrt{3})}^{2} + {(y - 3)}^{2} = 4

cut the line joining their centers at

B

and

C

, then triangle

B A C

is a/an

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 4 - Circles>DPP>Q 4

Suppose that two circles

C_{1}

and

C_{2}

in a plane have no points in common, then

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 4 - Circles>DPP>Q 5

A circle of radius

2

has its centre at

(2, 0)

and another circle of radius

1

has its centre at

(5, 0)

. A line is a tangent to the two circles at points in the first quadrant. The

y

-intercept of the tangent line is

The line y=mx intersects the circle x2+y2-2x-2y=0 and x2+y2+6x-8y=0 at points A and B (points being other than origin). The range of m such that origin divides AB internally is

Important Questions on Circles

Learn and Prepare for any exam you want !

The line $y = m x$ intersects the circle $x^{2} + y^{2} - 2 x - 2 y = 0$ and $x^{2} + y^{2} + 6 x - 8 y = 0$ at points $A$ and $B$ (points being other than origin). The range of $m$ such that origin divides $A B$ internally is