Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 13

HARD

JEE Main

IMPORTANT

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Two fixed circles with radii $r_{1}$ and $r_{2} (r_{1} > r_{2})$ respectively touch each other externally. Then the locus of the point of intersection of their direct common tangents is

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Important Questions on Circle

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 14

Two circles with radii

a

and

b

touch each other externally such that

θ

is the angle between the direct common tangents

(a > b \geq 2)

, then

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 16

Equation of a circle that cuts the circle

x^{2} + y^{2} + 2 g x + 2 f y + c = 0

, lines

x = g

and

y = f

orthogonally is

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 19

f (x, y) = 0

is a circle such that

f (0, λ) = 0

and

f (λ, 0) = 0

have equal roots and

f (1, 1) = - 2

then the radius of the circle is

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JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 20

2 x^{2} + 2 y^{2} + 4 λ x + λ = 0

represents a circle for

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 21

The locus of the mid-point of a chord of the circle $x^{2} + y^{2} - 2 x - 2 y - 23 = 0$ of length $8$ units is

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 22

The equation of the circle having the intercept on the line

y + 2 x = 0

by the circle

x^{2} + y^{2} + 4 x + 6 y = 0

as a diameter is

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 23

If the tangent at

(1, 2)

to the circle

C_{1} : x^{2} + y^{2} = 5

intersects the circle

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

at

A

and

B

and tangents at

A

and

B

to the second circle meet at point

C

, then the coordinates of

C

are given by

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 24

The values of $' a'$ for which the common chord of the circles $x^{2} + y^{2} = 8$ and ${(x - a)}^{2} + y^{2} = 8$ subtends a right angle at the origin are