Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 55

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The length of the diameter of the circle which cuts three circles $x^{2} + y^{2} - x - y - 14 = 0, x^{2} + y^{2} + 3 x - 5 y - 10 = 0, x^{2} + y^{2} - 2 x + 3 y - 27 = 0$ orthogonally 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 1

The point of intersection of the lines

x - y + 1 = 0

and

x + y + 5 = 0

is

P .

A circle with centre at

(1, 0)

passes through

P .

The tangent to the circle at

P

meets the

x -

axis at

(k, 0) .

The value of

k

is

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

The area of a square circumscribing the circle

3 (x^{2} + y^{2}) - 6 x + 8 y = 0

is

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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