MEDIUM

JEE Main

IMPORTANT

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For $t \in (0, 2 π)$ , if $A B C$ is an equilateral triangle with vertices $A (\sin t, - \cos t), B (\cos t, \sin t)$ and $C (a, b)$ such that its orthocentre lies on a circle with centre $(1, \frac{1}{3})$ , then $(a^{2} - b^{2})$ is equal to

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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 - 28 July 2022 Shift 2>Q 91

Let the tangents at two points

A

and

B

on the circle

x^{2} + y^{2} - 4 x + 3 = 0

meet at origin

O (0, 0)

. Then the area of the triangle of

O A B

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 29 July 2022 Shift 1>Q 92

Let the mirror image of a circle

c_{1} : x^{2} + y^{2} - 2 x - 6 y + α = 0

in line

y = x + 1

c_{2} : 5 x^{2} + 5 y^{2} + 10 g x

+ 10 f y + 38 = 0

. If

r

is the radius of circle

c_{2}

, then

α + 6 r^{2}

is equal to ______

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 29 July 2022 Shift 2>Q 93

Let

A B

be a chord of length

12

of the circle

{(x - 2)}^{2} + {(y + 1)}^{2} = \frac{169}{4}

. If tangents drawn to the circle at points

A

and

B

intersect at the point

P

, then five times the distance of point

P

from chord

A B

is equal to _____.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 24 January 2023 Shift 2>Q 94

The locus of the middle points of the chords of the circle

C_{1} : {(x - 4)}^{2} + {(y - 5)}^{2} = 4

which subtend an angle

θ_{i}

at the centre of the circle

C_{i}

, is a circle of radius

r_{i}

. If

θ_{1} = \frac{π}{3}

θ_{3} = \frac{2 π}{3}

and

{r_{1}}^{2} = {r_{2}}^{2} + {r_{3}}^{2}

, then

θ_{2}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 25 January 2023 Shift 1>Q 95

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 :

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

For t∈0,2π, if ABC is an equilateral triangle with vertices Asint,-cost,Bcost,sint and Ca,b such that its orthocentre lies on a circle with centre 1,13, then a2-b2 is equal to

Important Questions on Circle

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For $t \in (0, 2 π)$ , if $A B C$ is an equilateral triangle with vertices $A (\sin t, - \cos t), B (\cos t, \sin t)$ and $C (a, b)$ such that its orthocentre lies on a circle with centre $(1, \frac{1}{3})$ , then $(a^{2} - b^{2})$ is equal to