Let P and Q be two distinct points on a circle which has center at C 2 , 3 and which passes through origin O . If O C is perpendicular to both the line segments C P and C Q , then the set P , Q is equal to

2 + 2 2 , 3 - 5 , 2 - 2 2 , 3 + 5

2 + 2 2 , 3 + 5 , 2 - 2 2 , 3 - 5

MEDIUM

JEE Main

IMPORTANT

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Let the circle $S : 36 x^{2} + 36 y^{2} - 108 x + 120 y + C = 0$ be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, $x - 2 y = 4$ and $2 x - y = 5$ lies inside the circle $S,$ then:

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Important Questions on Circle

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 27 July 2021 Shift 1>Q 9

Two tangents are drawn from the point

P (- 1, 1)

to the circle

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

If these tangents touch the circle at points

A

and

B,

and if

D

is a point on the circle such that length of the segments

A B

and

A D

are equal, then the area of the triangle

A B D

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 27 July 2021 Shift 1>Q 10

Let

P

and

Q

be two distinct points on a circle which has center at

C (2, 3)

and which passes through origin

O .

O C

is perpendicular to both the line segments

C P

and

C Q,

then the set

\{P, Q\}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 27 July 2021 Shift 1>Q 11

Let

$A = \{(x, y) \in R \times R ∣ 2 x^{2} + 2 y^{2} - 2 x - 2 y = 1\}$

$B = \{(x, y) \in R \times R ∣ 4 x^{2} + 4 y^{2} - 16 y + 7 = 0\}$ and

$C = \{(x, y) \in R \times R ∣ x^{2} + y^{2} - 4 x - 2 y + 5 \leq r^{2}\}$ . Then the minimum value of $|r|$ such that $A \cup B \subseteq C$ is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 27 July 2021 Shift 2>Q 12

Consider a circle

C

which touches the

y -

axis at

(0, 6)

and cuts off an intercept

6 \sqrt{5}

on the

x -

axis. Then the radius of the circle

C

is equal to :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main 16 March 2021 Shift 1>Q 13

Let

A B C D

be a square of side of unit length. Let a circle

C_{1}

centered at

A

with unit radius is drawn. Another circle

C_{2}

which touches

C_{1}

and the lines

A D

and

A B

are tangent to it, is also drawn. Let a tangent line from the point

C

to the circle

C_{2}

meet the side

A B

E

. If the length of

E B

α + \sqrt{3} β

, where

α, β

are integers, then

α + β

is equal to ________.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main 16 March 2021 Shift 2>Q 14

Let the lengths of intercepts on

x

-axis and

y

-axis made by the circle

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

(a < 0)

2 \sqrt{2}

and

2 \sqrt{5}

, respectively. Then the shortest distance from origin to a tangent to this circle which is perpendicular to the line

x + 2 y = 0,

is equal to :

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main 17 March 2021 Shift 1>Q 15

The line

2 x - y + 1 = 0

is a tangent to the circle at the point

(2, 5)

and the centre of the circle lies on

x - 2 y = 4 .

Then, the radius of the circle is:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main 17 March 2021 Shift 1>Q 16

Choose the incorrect statement about the two circles whose equations are given below:

$x^{2} + y^{2} - 10 x - 10 y + 41 = 0$ and $x^{2} + y^{2} - 16 x - 10 y + 80 = 0$

Let the circle S:36x2+36y2-108x+120y+C=0 be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, x-2y=4 and 2x-y=5 lies inside the circle S, then:

Important Questions on Circle

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Let the circle $S : 36 x^{2} + 36 y^{2} - 108 x + 120 y + C = 0$ be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, $x - 2 y = 4$ and $2 x - y = 5$ lies inside the circle $S,$ then: