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

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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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Important Questions on Ellipse

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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

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-3>Q 11

The tangent and normal to the ellipse

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

at a point

P (θ)

on it meet the major axis in

Q

and

R

respectively. If

Q R = 2

and the eccentric angle

θ

of

P

is given by

\cos θ = \pm (\frac{a}{b})

, where

a

&

b

are relative prime, then value of

\frac{b}{a}

is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-3>Q 12

If

3 x + 4 y = 12

intersect the ellipse

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

at

P

and

Q

. If the point of intersection of tangents at

P

and

Q

is

(\frac{25}{a}, \frac{16}{b})

, then

a + b

is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-4>Q 1

Find the co-ordinates of all the points

P

on the ellipse

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

for which the area of the triangle

P O N

is maximum, where

O

denotes the origin and

N

the foot of the perpendicular from

O

to the tangent at

P

.

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-4>Q 2

Find the equation of the ellipse, whose focus is the point

(- 1, 1)

, with respective directrix having equation

x - y + 3 = 0

, and whose eccentricity is

\frac{1}{2} .

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-4>Q 3

Find the latus rectum, eccentricity, coordinates of the foci, coordinates of the vertices, the length of the axes and the centre of the ellipse

4 x^{2} + 9 y^{2} - 8 x - 36 y + 4 = 0

.

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-4>Q 4

Find the condition so that the line

p x + q y = r

intersects the ellipse

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

in points whose eccentric angles differ by

\frac{π}{4}

.