EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 10th April 2019 Shift 1>Q 48

MEDIUM

JEE Main

IMPORTANT

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If the circles $x^{2} + y^{2} + 5 K x + 2 y + K = 0$ and $2 (x^{2} + y^{2}) + 2 K x + 3 y - 1 = 0, (K \in R)$ , intersect at the points $P & Q$ , then the line $4 x + 5 y - K = 0$ , passes through $P$ and $Q,$ for:

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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 - 10th April 2019 Shift 2>Q 49

The locus of the centres of the circles, which touch the circle,

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

externally, also touch the

y

-axis and lie in the first quadrant, is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 10th January 2019 Shift 1>Q 50

If a circle

C

passing through the point

(4, 0)

touches the circle

x^{2} + y^{2} + 4 x - 6 y = 12

externally at the point

(1, - 1),

then the radius of

C

is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 10th January 2019 Shift 2>Q 51

If the area of an equilateral triangle inscribed in the circle

x^{2} + y^{2} + 10 x + 12 y + c = 0

is

27 \sqrt{3} sq . units,

then

c

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 12th April 2019 Shift 1>Q 52

If the angle of intersection at a point where the two circles with radii

5 c m

and

12 c m

intersect is

90 °

, then the length (in cm) of their common chord is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 12th April 2019 Shift 2>Q 53

A circle touching the

x -

axis at

(3, 0)

and making an intercept of length

8

on the

y -

axis passes through the point:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 12th January 2019 Shift 1>Q 54

Let

C_{1}

and

C_{2}

be the centres of the circles

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

and

x^{2} + y^{2} - 6 x - 6 y + 14 = 0

respectively. If

P

and

Q

are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral

P C_{1} Q C_{2}

is :

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 12th January 2019 Shift 1>Q 55

If a variable line

3 x + 4 y - λ = 0

is such that the two circles

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

and

x^{2} + y^{2} - 18 x - 2 y + 78 = 0

are on its opposite sides, then the set of all values of

λ

is the interval :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 15th April 2018>Q 56

A circle passes through the points

(2, 3)

and

(4, 5)

. If its centre lies on the line

y - 4 x + 3 = 0

, then its radius is equal to :