Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 36

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If the focal distance of an end of the minor axis of an ellipse, whose axes along the $x$ and $y$ axes respectively is $k$ and the distance between the foci is $2 h$ . Then the equation of the ellipse 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 38

The number of values of

c

, such that

y = 4 x + c

touches

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

, is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 40

The line

2 x + y = 3

cuts the ellipse

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

at

P

and

Q

. If $\theta$ be the angle between the normals at these points, then

\tan θ

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 41

Number of points on the ellipse

\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1

from which pair of perpendicular tangents are drawn to the ellipse

\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1

, 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