Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 48

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The image of the centre of a circle $(x - 2)^{2} + (y - 1)^{2} = 9$ w.r.t. the line $y = x$ moves $\sqrt{2}$ units along $(N - E)$ direction then the co-ordinates of the centre in the new position 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 49

The equation of the circle whose radius is

5

and which touches the circle

x^{2} + y^{2} - 2 x - 4 y - 20 = 0

externally at the point

(5, 5)

, is

x^{2} + y^{2} - 18 x + λ y + μ = 0

then

(λ + μ)

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 50

A circle has radius

3

units and its centre lies on the line

y = x - 1

. If the circle passes through point

(7, 3)

and has centre at point

(h, k)

then

h^{k}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 53

The equation of the circle having the lines

x^{2} + 2 x y + 3 x + 6 y = 0

as its normals and having size just sufficient to contain the circle

x (x - 4) + y (y - 3) = 0

is

x^{2} + y^{2} + λ x - 3 y - μ = 0

, where

λ, μ \in N,

then

(λ + μ)

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 54

If the circles of same radius

a

and centres at

(2, 3)

and

(5, 6)

cut orthogonally, then

a

is equal to

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

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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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