Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-2>Q 14

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If latus rectum of an ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{b^{2}} = 1 {0 < b < 4}$ , subtend angle $2 θ$ at farthest vertex such that $cosec θ = \sqrt{5}$ , then -

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Important Questions on Ellipse

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-2>Q 15

If

x - 2 y + k = 0

is a common tangent to

y^{2} = 4 x

&

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{3} = 1 (a > \sqrt{3})

, then the value of

a, k

and other common tangent are given by -

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-2>Q 16

All ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 (0 < b < a)

has fixed major axis. Tangent at any end point of latus rectum meet at a fixed point which can be -

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-2>Q 17

Eccentric angle of a point on the ellipse

x^{2} + 3 y^{2} = 6

at a distance

\sqrt{3}

units from the centre of the ellipse is -

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-2>Q 18

For the ellipse

9 x^{2} + 16 y^{2} - 18 x + 32 y - 119 = 0

, which of the following is/are true -

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-2>Q 19

With respect to the ellipse

4 x^{2} + 7 y^{2} = 8

, the correct statement(s) is/are -

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-3>Q 8

Eccentricity of an ellipse in which distance between their foci is

10

and that of focus and corresponding directrix is

15

is equal to:

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-3>Q 9

An ellipse passes through the points

(- 3, 1)

&

(2, - 2)

its principal axis are along the coordinate axes in order. The value of

{(length of semi - minor axis)}^{2}

is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-3>Q 10

If set of value(s) of

α

for which the point

(7 - \frac{5}{4} α, α)

lies inside the ellipse

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

is

(\frac{12}{λ}, \frac{16}{λ})

, then value of

λ

is