Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-1>Q 36

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The tangent from the point of intersection of the lines $2 x - 3 y + 1 = 0$ and $3 x - 2 y - 1 = 0$ to the circle $x^{2} + y^{2} + 2 x - 4 y = 0$ is

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Important Questions on Circle

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-1>Q 37

The locus of the centres of the circles which cut the circles

x^{2} + y^{2} + 4 x - 6 y + 9 = 0

and

x^{2} + y^{2} - 5 x + 4 y + 2 = 0

orthogonally is-

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-2>Q 1

Let

f (x) = x^{2} + 6 x + 1

and

R

denote the set of points

(x, y)

in the coordinate plane such that

f (x) + f (y) \leq 0

and

f (x) - f (y) \leq 0

. The area of

R

is equal to -

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-2>Q 2

If

(a, \frac{1}{a}), (b, \frac{1}{b}), (c, \frac{1}{c}) & (d, \frac{1}{d})

are four distinct points on a circle of radius

4

units then,

a b c d =

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-2>Q 3

Three equal circles each of radius

r

touch one another. The radius of the circle touching all the three given circles internally is

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-2>Q 5

The distance between the chords of contact of tangents to the circle

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

from the origin and from the point

(g, f)

is

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-2>Q 6

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

and

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

are two circles, then

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-2>Q 7

Tangents are drawn to the circle

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

at the points where it is met by the circles,

x^{2} + y^{2} - (λ + 6) x + (8 - 2 λ) y - 3 = 0, λ

being the variable. The locus of the point of intersection of these tangents is

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-2>Q 8

3

circle of radii

1, 2

and

3

and centres at

A, B

and

C

respectively, touch each other. Another circle whose centre is

P

touches all these

3

circles externally and has radius

r

. Also

∠ P A B = θ & ∠ P A C = α