EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 26 August 2021 Shift 2>Q 1

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IMPORTANT

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A circle $C$ touches the line $x = 2 y$ at the point $(2, 1)$ and intersects the circle $C_{1} : x^{2} + y^{2} + 2 y - 5 = 0$ at two points $P$ and $Q$ such that $P Q$ is a diameter of $C_{1}$ . Then the diameter of $C$ is :

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Important Questions on Circle

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 31 August 2021 Shift 2>Q 5

Let

B

be the centre of the circle

x^{2} + y^{2} - 2 x + 4 y + 1 = 0 .

Let the tangents at two points

P

and

Q

on the circle intersect at the point

A (3, 1) .

Then

8 (\frac{area Δ APQ}{area Δ BPQ})

is equal to .

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 31 August 2021 Shift 1>Q 4

If the variable line

3 x + 4 y = α

lies between the two circles

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

and

(x - 9)^{2} + (y - 1)^{2} = 4,

without intercepting a chord on either circle, then the sum of all the integral values of

α

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 2 September 2020 Shift 1>Q 29

The numbers of integral values of

k

for which the line,

3 x + 4 y = k

intersects the circle,

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

at two distinct points is....

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 4 September 2020 Shift 2>Q 32

The circle passing through the intersection of the circles,

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

and

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

having its centre on the line,

2 x - 3 y + 12 = 0

, also passes through the point :

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 9th January 2020 Shift 1>Q 38

A circle touches the

y

-axis at the point

(0, 4)

and passes through the point

(2, 0)

. Which of the following lines is not a tangent to this circle?

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 9th January 2020 Shift 2>Q 39

If the curves,

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

and

x^{2} - 8 y + y^{2} + 16 - k = 0, (k > 0)

touch each other at a point, then the largest value of

k

is ____________.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 9th April 2019 Shift 2>Q 42

The area (in sq. units) of the smaller of the two circles that touch the parabola,

y^{2} = 4 x

at the point

(1, 2)

and the

x

-axis is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 10th April 2019 Shift 1>Q 47

The line

x = y

touches a circle at the point

(1, 1)

. If the circle also passes through the point

(1, - 3)

, then its radius is