Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 2

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The area of a square circumscribing the circle $3 (x^{2} + y^{2}) - 6 x + 8 y = 0$ 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 4

If the circle

O : x^{2} + y^{2} = 16

intersects another circle

C

of radius

5

units in such a way that the common chord is of maximum length and has a slope equal to

\frac{3}{4},

then the coordinates of the centre of

C

are

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 5

The equation of a circle which passes through

(2 a, 0)

and whose radical axis in relation to the circle

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

is

x = \frac{a}{2},

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 6

Two rods of lengths

a

and

b

slide along the

x

-axis and

y

-axis respectively in such a manner that their ends are concylic. The locus of the centre of the circle passing through the end points is

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

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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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