Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 46

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For the circles $x^{2} + y^{2} - 10 x + 16 y + 89 - r^{2} = 0$ and $x^{2} + y^{2} + 6 x - 14 y + 42 = 0$ which of the following is/are trüe?

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Important Questions on Circle

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 47

Which of the following statement

(s)

is/are correct with respect to the circles

S_{1} \equiv x^{2} + y^{2} - 4 = 0

and

S_{2} \equiv x^{2} + y^{2} - 2 x - 4 y + 4 = 0 ?

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 48

Two circles, each of radius

5

units, touch each other at

(1, 2) .

If the equation of their common tangent is

4 x + 3 y = 10 .

The equations of the circles are

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 49

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

and

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

are two equal circles touching each other. Find the equation of circle (or circles) of the same radius touching both the circles.

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 50

The circle

x^{2} + y^{2} - 2 x - 3 k y - 2 = 0

passes through two fixed points,

(k

is the parameter)

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 51

Curves

a x^{2} + 2 h x y + b y^{2} - 2 g x - 2 f y + c = 0

and

a^{'} x^{2} - 2 h x y + (a^{'} + a - b) y^{2} - 2 g^{'} x - 2 f^{'} y + c = 0

intersect at four concyclic points

A, B, C

and

D

. If

P

be the point

(\frac{g^{'} + g}{a^{'} + a}, \frac{f^{'} + f}{a^{'} + a})

, then which of the following is/are true

?

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 54

Set of values of

m

for which a chord of slope

m

of the circle

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

touches parabola

y^{2} = 4 x

, may lie in interval

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-3>Q 1

Three distinct points

A, B

and

C

are given in the

2

-dimensional coordinate plane such that the ratio of the distance of any one of them from the point

(1, 0)

to the distance from the point

(- 1, 0)

is equal to

\frac{1}{3}

. Then the circumcentre of the triangle

A B C

is at the point

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-3>Q 2

Tangents drawn from the point $P (1, 8)$ to the circle $x^{2} + y^{2} - 6 x - 4 y - 11 = 0$ touch the circle at points $A$ and $B$ . The equation of the circumcircle of triangle $P A B$ is