EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 9th January 2019 Shift 2>Q 44

HARD

JEE Main

IMPORTANT

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If the circles $x^{2} + y^{2} - 16 x - 20 y + 164 = r^{2}$ and ${(x - 4)}^{2} + {(y - 7)}^{2} = 36$ intersect at two distinct points, then:

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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 - 8th April 2019 Shift 1>Q 45

The sum of the squares of the lengths of the chords intercepted on the circle,

x^{2} + y^{2} = 16,

by the lines,

x + y = n, n \in N,

where

N

is the set of all natural numbers is:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circle>JEE Main - 8th April 2019 Shift 2>Q 46

The tangent and the normal lines at the point

(\sqrt{3}, 1)

to the circle

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

and the

x

-axis form a triangle. The area of this triangle (in square units) is:

MEDIUM

JEE Main

IMPORTANT

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

MEDIUM

JEE Main

IMPORTANT

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

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:

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: