Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-1>Q 30

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The equation of the circle having the lines $y^{2} - 2 y + 4 x - 2 x y = 0$ as its normals & passing through the point $(2, 1)$ 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 31

A circle is drawn touching the

x

-axis and centre at the point which is the reflection of

(a, b)

in the line

y - x = 0

. The equation of the circle is

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-1>Q 32

The length of the common chord of circles

x^{2} + y^{2} - 6 x - 16 = 0

and

x^{2} + y^{2} - 8 y - 9 = 0

is

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-1>Q 33

The number of common tangents of the circles

x^{2} + y^{2} - 2 x - 1 = 0

and

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

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-1>Q 34

If the circle

x^{2} + y^{2} = 9

touches the circle

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

, then

c

is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-1>Q 35

If the two circles,

x^{2} + y^{2} + 2 g_{1} x + 2 f_{1} y = 0

and

x^{2} + y^{2} + 2 g_{2} x + 2 f_{2} y = 0

touches each other, then

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

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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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 -