Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-1>Q 2

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If the eccentricity of an ellipse be $\frac{5}{8}$ and the distance between its foci be $10$ , then its latus rectum is

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Important Questions on Ellipse

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-1>Q 3

The curve represented by

x = 3 (\cos t + \sin t)

,

y = 4 (\cos t - \sin t)

is

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

If the distance of a point on the ellipse

\frac{x^{2}}{6} + \frac{y^{2}}{2} = 1

from the centre is

2,

then the eccentric angle is-

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-1>Q 5

An ellipse having foci at

(3, 3)

and

(- 4, 4)

and passing through the origin has eccentricity equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-1>Q 6

A tangent having slope of

- \frac{4}{3}

to the ellipse

\frac{x^{2}}{18} + \frac{y^{2}}{32} = 1

intersects the major and minor axes in points

A

and

B

respectively. If

C

is the centre of the ellipse then the area of the triangle

A B C

is :

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-1>Q 7

The equation to the locus of the middle point of the portion of the tangent to the ellipse

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

included between the co-ordinate axes is the curve

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-1>Q 8

An ellipse is drawn with major and minor axes of lengths

10

and

8

respectively. Using one focus as centre, a circle is drawn that is tangent to the ellipse, with no part of the circle being outside the ellipse. The radius of the circle is-

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-1>Q 9

Which of the following is the common tangent to the ellipses

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

and

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

?

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-1>Q 10

Angle between the tangents drawn from point

(4, 5)

to the ellipse

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

is: