Mathematics Crash Course BITSAT>Chapter 9 - Circle>Exercise 1>Q 50

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The chord of contact of tangents from a point $P$ to a circle passes through $Q$ . If $l_{1}$ and $l_{2}$ are the lengths of the tangents from $P$ and $Q$ to the circle, then $P Q$ is equal to

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Important Questions on Circle

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Mathematics Crash Course BITSAT>Chapter 9 - Circle>Exercise 1>Q 51

If a circle passes through the points where the lines

3 k x - 2 y - 1 = 0

and

4 x - 3 y + 2 = 0

meet the coordinate axes, then

k =

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Mathematics Crash Course BITSAT>Chapter 9 - Circle>Exercise 1>Q 52

Inside the circle

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

, there are three smaller circles of equal radius

a

, touching each other and also touching the circle

S

. The value of

a

equals to

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Mathematics Crash Course BITSAT>Chapter 9 - Circle>Exercise 1>Q 53

A circle of radius

2

has its centre at

(2, 0)

and another circle of radius

1

has its centre at

(5, 0)

. A line is a tangent to the two circles at points in the first quadrant. The

y

-intercept of the tangent line is

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Mathematics Crash Course BITSAT>Chapter 9 - Circle>Exercise 1>Q 54

If two circles

a (x^{2} + y^{2}) + b x + c y = 0

and

A (x^{2} + y^{2}) + B x + C y = 0

touch each other, then

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Mathematics Crash Course BITSAT>Chapter 9 - Circle>Exercise 1>Q 55

If the circumference of the circle

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

is bisected by the circle

x^{2} + y^{2} - 2 x + 4 y + a = 0,

then

a + b

equals to

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Mathematics Crash Course BITSAT>Chapter 9 - Circle>Exercise 1>Q 56

The centre of the circle

(x - α)^{2} + (y - β)^{2} = 9

lies on the straight line

x = y

and the circle touches the circle

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

externally. What are the values of

α, β ?

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Mathematics Crash Course BITSAT>Chapter 9 - Circle>Exercise 1>Q 57

The angle of intersection of the circles

x^{2} + y^{2}

- x + y - 8 = 0

and

x^{2} + y^{2} + 2 x + 2 y - 11 = 0

is

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Mathematics Crash Course BITSAT>Chapter 9 - Circle>Exercise 1>Q 58

The coordinates of two points

P

and

Q

are

(x_{1}, y_{1})

and

(x_{2}, y_{2})

and

O

is the origin. If circles be described on

O P

and

O Q

as diameters, then the length of their common chord is