EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 26 Feb 2021 Shift 1>Q 25

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JEE Main

IMPORTANT

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In the circle given below, let $O A = 1$ unit, $O B = 13$ unit and $P Q ⊥ O B$ . Then, the area of the triangle $P Q B$ (in square units) is :

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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 - 26 Feb 2021 Shift 2>Q 26

If the locus of the mid-point of the line segment from the point

(3, 2)

to a point on the circle,

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

is a circle of radius

r

, then

r

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 26 Feb 2021 Shift 2>Q 27

Let

A (1, 4)

and

B (1, - 5)

be two points. Let

P

be a point on the circle

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

, such that

{(P A)}^{2} + {(P B)}^{2}

have maximum value, then the points,

P, A

and

B

lie on

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 26 Feb 2021 Shift 2>Q 28

Let the normals at all the points on a given curve pass through a fixed point

(a, b)

. If the curve passes through

(3, - 3)

and

(4, - 2 \sqrt{2})

, given that

a - 2 \sqrt{2} b = 3

, then

(a^{2} + b^{2} + a b)

is equal to _____.

MEDIUM

JEE Main

IMPORTANT

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 - 3 September 2020 Shift 1>Q 30

The diameter of the circle, whose Centre lies on the line

x + y = 2

in the first quadrant and which touches both the lines

x = 3

and

y = 2

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 3 September 2020 Shift 2>Q 31

Let the latus rectum of the parabola $y^{2} = 4 x$ be the common chord to the circles $C_{1}$ and $C_{2}$ each of them having radius $2 \sqrt{5}$ . Then, the distance between the centres of the circles $C_{1}$ and $C_{2}$ 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 :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 4 September 2020 Shift 2>Q 33

Let

P Q

be a diameter of the circle

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

. If

α

and

β

are the lengths of the perpendiculars from

P

and

Q

on the straight line,

x + y = 2

respectively, then the maximum value of

α β

is _______