Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.3>Q 21

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Length of the latus-rectum of the ellipse represented by $x = 3 (\cos t + \sin t), y = 4 (\cos t - \sin t);$ 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>EXERCISE 13.3>Q 22

The number of values of

c

such that the straight line

y = 4 x + c

touches the curve

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

is -

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.3>Q 23

Tangents are drawn to the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{5} = 1$ at the ends of latus rectum. The area of quadrilateral so formed is (in sq. units)

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.3>Q 24

If tangents are drawn to the ellipse

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

then the locus of mid points of the intercept made by the tangents between the co-ordinate axes, is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.3>Q 25

If the line

p x + q y = r

intersects the ellipse

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

in points, whose eccentric angles differ by

\frac{π}{3},

then

r^{2}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.3>Q 26

Minimum area of the triangle formed by any tangent to the ellipse

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

with the coordinate axes is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.3>Q 27

Product of the perpendiculars drawn from the foci upon any tangent to the ellipse

3 x^{2} + 4 y^{2} = 12

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.3>Q 28

The line

l x + m y + n = 0

is a normal to the ellipse

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

if

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.3>Q 29

If the normal to the ellipse

\frac{x^{2}}{14} + \frac{y^{2}}{5} = 1

at the point

θ

intersects the curve again at the point

2 θ,

then cos

θ

is equal to