Mathematics Crash Course JEE Main>Chapter 4 - Circle>Level 1>Q 21

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JEE Main

IMPORTANT

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If the circumference of the circle $x^{2} + y^{2} + 8 x + 8 y - b = 0$ is bisected by the circle $x^{2} + y^{2} - 2 x + 4 y + a = 0,$ then $a + b$ equals to

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Important Questions on Circle

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 4 - Circle>Level 1>Q 22

The centre of the circle

(x - α)^{2} + (y - β)^{2} = 9

lies on the straight line

x = y

and the circle touches the circle

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

externally. What are the values of

α, β ?

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 4 - Circle>Level 1>Q 23

The angle of intersection of the circles

x^{2} + y^{2}

- x + y - 8 = 0

and

x^{2} + y^{2} + 2 x + 2 y - 11 = 0

is

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 4 - Circle>Level 1>Q 24

If one of the diameters of the circle

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

is a chord of another circle

{}^{'}C^{'}

, whose center is at

(2, 1)

, then its radius is_____.

EASY

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 4 - Circle>Level 1>Q 25

The minimum distance between any two points $P_{1}$ and $P_{2}$ while considering point $P_{1}$ on one circle and point $P_{2}$ on the other circle for the given circles' equations

$x^{2} + y^{2} - 10 x - 10 y + 41 = 0$

$x^{2} + y^{2} - 24 x - 10 y + 160 = 0$ is ________

HARD

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 4 - Circle>Level 1>Q 26

The equation of the circle having

x - y - 2 = 0

and

x - y + 2 = 0

as two tangents and

x + y = 0

as a diameter is

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 4 - Circle>Level 1>Q 27

Let

A

be the centre of the circle

x^{2} + y^{2} - 2 x - 4 y - 20 = 0,

and

B (1, 7)

and

D (4, - 2)

are points on the circle, then, if tangents are drawn at

B

and

D,

which meet at

C,

then area of quadrilateral

A B C D

is

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 4 - Circle>Level 1>Q 28

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

Mathematics Crash Course JEE Main>Chapter 4 - Circle>Level 1>Q 29

The equation of the circle through the intersection of the circles

x^{2} + y^{2} - 8 x - 2 y + 7 = 0

and

x^{2} + y^{2} - 4 x + 10 y + 8 = 0

and that passes through the point

(- 1, - 2)

, is