Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 3

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The equation of the tangent to the circle $x^{2} + y^{2} + 4 x - 4 y + 4 = 0$ which makes equal intercepts on the coordinate axes is given by

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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 5

Equation of a circle through the origin, making an intercept of

\sqrt{10}

on the line

y = 2 x + \frac{5}{\sqrt{2}}

and this intercept subtends an angle of

45 °

at the origin, is

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

The equation of common tangent to the circles

x^{2} + y^{2} - 2 x - 6 y + 9 = 0

and

x^{2} + y^{2} + 6 x - 2 y + 1 = 0

is

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

If the circles

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

and

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

touch each other, then

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

If

(a \cos θ_{1}, a \sin θ_{1}), (a \cos θ_{2}, a \sin θ_{2}), (a \cos θ_{3}, a \sin θ_{3})

represents the vertices of an equilateral triangle inscribed in

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

then

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 12

The locus of the centre of the circle which moves such that it touches the circle

(x + 1)^{2} + y^{2} = 1

externally and also the

y

-axis is

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

Tangents and normal are drawn from a point

P (3, 1)

to circle

C

whose equation is

x^{2} + y^{2} - 2 x - 2 y + 1 = 0 .

Let the points of contact of tangents be

T_{i}

(x_{i}, y_{i}),

where

i = 1, 2

and feet of normals be

N_{1}

and

N_{2} (N_{1}

is near

P) .

Tangents are drawn at

N_{1}

and

N_{2}

and normals are drawn at

T_{1}

and

T_{2}

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

Let

C_{1}

and

C_{2}

be two concentric circles such that the radius of

C_{2}

is double that of radius of

C_{1} .

Tangents

P Q

and

P R

are drawn from a point on

C_{2}

to

C_{1}

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 16

Chords are drawn to the circle

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

from the point

(- 1, - 1) .

If circle cuts off equal intercept on these chords and the line

3 x + 4 y + 3 = 0,

then the equation of chord

(s)

may be