Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-1>Q 69

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Two circles are drawn through the point $(a, 5 a)$ and $(4 a, a)$ to touch the axis of ${}^{'}y^{'} .$ They intersect at an angle of $θ$ then $\tan θ$ is

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Important Questions on Circle

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-1>Q 72

If a circle be drawn so as always to touch a given straight line and also a given circle externally then prove that the locus of its centre is a parabola. (given line and given circle are non-intersecting)

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-1>Q 73

A parabola

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

crosses the

x

-axis at

(α, 0) (β, 0)

both to the right of the origin. A circle also passes through these two points. Find the length of a tangent from the origin to the circle.

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-1>Q 74

Find the locus of the mid-points of the chords of the circle

x^{2} + y^{2} = 16,

which are tangent to the hyperbola

9 x^{2} - 16 y^{2} = 144

.

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 1

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

is equal to

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

From the point

A (0, 3)

on the circle

x^{2} + 4 x + {(y - 3)}^{2} = 0

, a chord

A B

is drawn

&

extended to a point

M

such that

A M = 2 A B

. The equation of the locus of

M

is

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

If the tangent at

(1, 2)

to the circle

C_{1} : x^{2} + y^{2} = 5

intersects the circle

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

at

A

and

B

and tangents at

A

and

B

to the second circle meet at point

C

, then the coordinates of

C

are given by

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 4

A circle passes through point $(3, \sqrt{\frac{7}{2}})$ touches the line pair $x^{2} - y^{2} - 2 x + 1 = 0 .$ Centre of circle lies inside the circle $x^{2} + y^{2} - 8 x + 10 y + 15 = 0 .$ Co-ordinate of centre of circle is

Note: Multiple options were correct, so changed one of the option.

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 5

The length of the tangents from any point on the circle

15 x^{2} + 15 y^{2} - 48 x + 64 y = 0

to the two circles

5 x^{2} + 5 y^{2} - 24 x + 32 y + 75 = 0

and

5 x^{2} + 5 y^{2} - 48 x + 64 y + 300 = 0

are in the ratio