Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>Multiple Choice II>Q 1

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If $O A$ and $O B$ are two perpendicular chords of the circle $r = a \cos θ + b \sin θ$ passing through origin, then the locus of the mid point of $A B$ is :

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Important Questions on Circle

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JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>Multiple Choice II>Q 2

If

A

and

B

are two points on the circle

x^{2} + y^{2} - 4 x + 6 y - 3 = 0

which are farthest and nearest respectively from the point

(7, 2)

, 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 4

The point

([P + 1], [P])

(where

[.]

denotes the greatest integer function), lying inside the region bounded by the circle

x^{2} + y^{2} - 2 x - 15 = 0

and

x^{2} + y^{2} - 2 x - 7 = 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 5

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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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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JEE Main/Advanced

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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

IMPORTANT

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 :