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

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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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Important Questions on Circle

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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

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-2>Q 9

Slope of tangent to the circle

{(x - r)}^{2} + y^{2} = r^{2}

at the point

(x, y)

lying on the circle is

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-2>Q 10

The circle passing through the distinct points

(1, t), (t, 1) & (t, t)

for all values of '

t

', circle passes through the point

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-2>Q 11

A B

is a diameter of a circle.

C D

is a chord parallel to

A B

and

2 C D = A B

. The tangent at

B

meets the line

A C

produced at

E

then

A E

is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-2>Q 12

The locus of the mid points of the chords of the circle

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

which subtend a right angle at

(\frac{a}{2}, \frac{b}{2})

is

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-2>Q 13

A variable circle is drawn to touch the

x

-axis at the origin. The locus of the pole of the straight line

l x + m y + n = 0

w.r.t. the variable circle has the equation