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

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IMPORTANT

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If $20 x^{2} - 4 y^{2} = 80$ represents the equation of a hyperbola, then find the length of its latus rectum.

Important Questions on Conic Section

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 4

Find the length of the latus rectum of the parabola

x^{2} = - 16 y .

EASY

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 5

If

\frac{x^{2}}{64} + \frac{y^{2}}{36} = 1

represents the equation of an ellipse, then find the distance between its foci.

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

Find the equation of the hyperbola with

y

-axis as its transverse axis whose length is

4

units and the length of conjugate axis as

6

units.

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

The length of the semi-minor axis of an ellipse with

x

-axis as the major axis is

3

units and the distance of the foci from the centre is

2 \sqrt{5} .

Find the equation of the ellipse.

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 8

If the equation of the parabola is

x^{2} = 24 y,

then find the co-ordinates of the focus and the length of the latus rectum.

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 9

For the hyperbola

25 y^{2} - 100 x^{2} = 100,

find the ecentricity and the co-ordinates of the vertices and the foci.

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 10

If the points

(0, 0)

and

(0, 7)

are respectively the vertex and focus of a parabola, then find the equation of the parabola, length of its latus rectum and equation of its directrix.

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IMPORTANT

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

If the eccentricity of an ellipse is

\frac{\sqrt{13}}{7}

and distance between its foci is

2 \sqrt{13},

then find the length of the latus rectum of the ellipse.