Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>INTRODUCTORY EXERCISE 4.5>Q 5

EASY

JEE Main/Advanced

IMPORTANT

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The tangents drawn from the origin to the circle $x^{2} + y^{2} - 2 k x - 2 r y + r^{2} = 0$ are perpendicular, if :

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Important Questions on Circle

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>INTRODUCTORY EXERCISE 4.5>Q 6

The length of tangent from

(0, 0)

to the circle

2 (x^{2} + y^{2}) + x - y + 5 = 0

is :

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>INTRODUCTORY EXERCISE 4.5>Q 7

Two perpendicular tangents to the circle

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

meet at

P

. Then the locus of

P

has the equation :

MEDIUM

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>INTRODUCTORY EXERCISE 4.5>Q 1

Distances from the origin to the centre of the three circles

x^{2} + y^{2} - 2 λ x = c^{2}

where

c

is a constant are in

GP

. Prove that the lengths of tangents drawn from any point on the circle

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

to the three circles are also in

GP

.

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>INTRODUCTORY EXERCISE 4.5>Q 3

If the length of the tangent from a point

(f, g)

to the circle

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

be four times the length of the tangent from it to the circle

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

, show that

15 f^{2} + 15 g^{2} - 64 f + 4 = 0

.

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>INTRODUCTORY EXERCISE 4.5>Q 4

Find the equation of that chord of the circle

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

which is bisected at

(3, 2)

.

MEDIUM

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>INTRODUCTORY EXERCISE 4.6>Q 1

Number of common real tangents that can be drawn to the circles

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

and

x^{2} + y^{2} - 8 x - 8 y + 14 = 0

is

MEDIUM

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>INTRODUCTORY EXERCISE 4.6>Q 2

The circles whose equations are

x^{2} + y^{2} + c^{2} = 2 a x

and

x^{2} + y^{2} + c^{2} - 2 b y = 0

will touch one another externally, if:

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>INTRODUCTORY EXERCISE 4.6>Q 4

The pole of the straight line

9 x + y - 28 = 0

with respect to the circle

2 x^{2} + 2 y^{2} - 3 x + 5 y - 7 = 0

is