Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 7

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The equation of the locus of the mid-points of chords of the circle $4 x^{2} + 4 y^{2} - 12 x + 4 y + 1 = 0$ that subtend an angle of $\frac{2 π}{3}$ at its centre, is

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Important Questions on Conic Section

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 8

The area of an equilateral triangle inscribed in the circle

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

is

\frac{m}{n} (a^{2} + b^{2} - c)

then the value of

\frac{1}{\sqrt{3}} m + n

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 9

The equation of the diameter of the circle

x^{2} + y^{2} + 2 g x + 2 f y + c = 0

which corresponds to the chord

a x + b y + d = 0

is

λ x - a y + μ g + k = 0

then

λ + μ

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 10

A line meets the co-ordinate axes at

A (a, 0)

and

B (0, b) .

A circle is circumscribed about the triangle

O A B .

If the distance of the points

A

and

B

from the tangent at origin to the circle are

3

and

4

respectively, then the value of

a^{2} + b^{2} + 1

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 11

A circle of constant radius

r

passes through the origin

O,

and cuts the axes at

A

and

B .

The locus of the foot of the perpendicular from

O

to

A B

is

{(x^{2} + y^{2})}^{k} = 4 r^{2} x^{2} y^{2},

then the value of

k

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 13

Four distinct points

(a, 0), (0, b), (c, 0)

and

(0, d)

are lie on a plane in such a way that

a c = b d,

then they will

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 14

A circle of radius

2

units touches the co-ordinate axes in first quadrant. If the circle moves one complete roll on

x -

axis along the positive direction of

x -

axis and then centre is rotated about the origin at

\frac{π}{3}

angle in anti-clockwise direction. Then, the co-ordinates of the centre in the new position is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 15

If the circle

x^{2} + y^{2} - 4 x - 8 y + 16 = 0

rolls up the tangent to it at

(2 + \sqrt{3}, 3)

by

2

units (assumes

x -

axis as horizontal), then the centre of the circle in the new position is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 1

If

α

is the angle subtended at

P (x_{1}, y_{1})

by the circle

S \equiv x^{2} + y^{2} + 2 g x + 2 f y + c = 0,

then