HARD

JEE Main

IMPORTANT

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Let $C$ be a circle passing through the points $A (2, - 1)$ and $B (3, 4)$ . The line segment $A B$ is not a diameter of $C$ . If $r$ is the radius of $C$ and its centre lies on the circle ${(x - 5)}^{2} + {(y - 1)}^{2} = \frac{13}{2}$ , then $r^{2}$ is equal to

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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 - 27 June 2022 Shift 1>Q 79

Let

\frac{d y}{d x} = \frac{a x - b y + a}{b x + c y + a}

, where

a, b, c

are constants. represent a circle passing through the point

(2, 5)

. Then the shortest distance of the point

(11, 6)

from this circle is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 27 June 2022 Shift 2>Q 80

The set of values of

k

for which the circle

C : 4 x^{2} + 4 y^{2} - 12 x + 8 y + k = 0

lies inside the fourth quadrant and the point

(1, - \frac{1}{3})

lies on or inside the circle

C

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 28 June 2022 Shift 1>Q 81

If the tangents drawn at the point

O (0, 0)

and

P (1 + \sqrt{5}, 2)

on the circle

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

intersect at the point

Q

, then the area of the triangle

O P Q

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 28 June 2022 Shift 1>Q 82

Let the lines

y + 2 x = \sqrt{11} + 7 \sqrt{7}

and

2 y + x = 2 \sqrt{11} + 6 \sqrt{7}

be normal to a circle

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

. If the line

\sqrt{11} y - 3 x = \frac{5 \sqrt{77}}{3} + 11

is tangent to the circle

C

, then the value of

{(5 h - 8 k)}^{2} + 5 r^{2}

is equal to ______.

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 28 June 2022 Shift 2>Q 83

If one of the diameters of the circle

x^{2} + y^{2} - 2 \sqrt{2} x

- 6 \sqrt{2} y + 14 = 0

is a chord of the circle

{(x - 2 \sqrt{2})}^{2}

+ {(y - 2 \sqrt{2})}^{2} = r^{2}

, then the value of

r^{2}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 29 June 2022 Shift 1>Q 84

Let the tangent to the circle

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

at the point

M (- 1, 1)

intersect the circle

C_{2}

{(x - 3)}^{2} + {(y - 2)}^{2} = 5

, at two distinct points

A

and

B

. If the tangents to

C_{2}

at the points

A

and

B

intersect at

N

, then the area of the triangle

A N B

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 29 June 2022 Shift 2>Q 85

Let a triangle

A B C

be inscribed in the circle

x^{2} - \sqrt{2} (x + y) + y^{2} = 0

such that

∠ B A C = \frac{π}{2}

. If the length of side

A B

\sqrt{2}

, then the area of the

△ A B C

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 25 July 2022 Shift 2>Q 86

If the circles

x^{2} + y^{2} + 6 x + 8 y + 16 = 0

and

x^{2} + y^{2} + 2 (3 - \sqrt{3}) x + 2 (4 - \sqrt{6}) y = k + 6 \sqrt{3} + 8 \sqrt{6}

k > 0

, touch internally at the point

P (α, β)

, then

{(α + \sqrt{3})}^{2} + {(β + \sqrt{6})}^{2}

is equal to _______.

Let C be a circle passing through the points A2,-1 and B3,4. The line segment AB is not a diameter of C. If r is the radius of C and its centre lies on the circle x-52+y-12=132, then r2 is equal to

Important Questions on Circle

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Let $C$ be a circle passing through the points $A (2, - 1)$ and $B (3, 4)$ . The line segment $A B$ is not a diameter of $C$ . If $r$ is the radius of $C$ and its centre lies on the circle ${(x - 5)}^{2} + {(y - 1)}^{2} = \frac{13}{2}$ , then $r^{2}$ is equal to