Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 43

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The equation of the chord of the ellipse $x^{2} + 4 y^{2} = 4$ having the middle point at $(- 1, \frac{1}{2})$ 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 44

Pole of the line $x+4 y=5$ with respect to the ellipse

5 x^{2} + 4 y^{2} = 10

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 45

The locus of the mid points of the portion of the tangents to the ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

intercepted between the axes is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 46

A rod of given length moves such that its extremities lie on two fixed perpendicular lines. Any point (other than mid point) on the rod describes

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 47

The locus of the feet of the perpendiculars drawn from the centre to the ellipse

\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1

on any tangent to it is

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

The locus of the foot of the perpendicular from any focus upon any tangent to

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 49

The locus of the foot of perpendicular from the centre on any tangent to the ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

is

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

The equation of the hyperbola whose foci are

(6, 4)

and

(- 4,4)

and eccentricity

2,

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 51

The equation of the hyperbola with centre at

(0, 0)

and co-ordinate axes as its axes, distance between the directrices being

\frac{4}{\sqrt{3}}

and passing through the point

(2, 1)

, is