Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>Multiple Choice II>Q 5

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If a chord of the circle $x^{2} + y^{2} - 4 x - 2 y - c = 0$ is trisected at $(\frac{1}{3}, \frac{1}{3})$ and $(\frac{8}{3}, \frac{8}{3})$ , then-

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Important Questions on Circle

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JEE Main/Advanced

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>Multiple Choice II>Q 6

From the point

A (0, 3)

on the circle

x^{2} + 4 x + {(y - 3)}^{2} = 0

, a chord $A B$ is drawn and extended to a point

M

such that

A M = 2 A B

. An equation of the locus of

M

is:

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>Multiple Choice II>Q 7

An equation of a circle touching the axes of co-ordinates and the line

x \cos α + y \sin α = 2

can be :

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>Multiple Choice II>Q 8

If

α

is the angle subtended at

P (x_{1}, y_{1})

by the circle

S \equiv x^{2} + y^{2} + 2 g x + 2 f y + c = 0,

then

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JEE Main/Advanced

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>Multiple Choice II>Q 9

The equation of the circle which touches the coordinate axes and the line

\frac{x}{3} + \frac{y}{4} = 1

and whose centre lies in the first quadrant is given by

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

where

λ

is equal to

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JEE Main/Advanced

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>Multiple Choice II>Q 10

If

P

is a point on the circle

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

is a point on the line

7 x + y + 3 = 0

and the line

x - y + 1 = 0

is the perpendicular bisector of

P Q

, then the co-ordinates of

P

are :

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JEE Main/Advanced

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>Multiple Choice II>Q 11

If a circle passes through the point

(3, \sqrt{\frac{7}{2}})

and touches

x + y = 1

and

x - y = 1

, then the centre of the circle is :

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JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>Multiple Choice II>Q 12

The equations of four circles are

{(x \pm a)}^{2} + {(y \pm a)}^{2} = a^{2}

. The radius of a circle touching all the four circles is:

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>Multiple Choice II>Q 13

The equation of a circle

C_{1}

is

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

The locus of the intersection of orthogonal tangents to the circle is the curve

C_{2}

and the locus of the intersection of perpendicular tangents to the curve

C_{2}

is the curve

C_{3} .

Then