Mathematics Crash Course NDA & NA EE>Chapter 13 - Ellipse>Exercise 1>Q 14

EASY

NDA & NA EE

IMPORTANT

Earn 100

What is the length of the latus rectum of an ellipse $25 x^{2} + 16 y^{2} = 400$ $?$

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Important Questions on Ellipse

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NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 13 - Ellipse>Exercise 1>Q 15

What is the equation of the ellipse whose vertices are

(\pm 5, 0)

and foci are at

(\pm 4, 0) ?

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NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 13 - Ellipse>Exercise 1>Q 16

If the distance between the directrices be thrice the distance between the foci, then the eccentricity of the ellipse is

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NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 13 - Ellipse>Exercise 1>Q 17

If the eccentricity of an ellipse be

\frac{1}{\sqrt{2}}

, then its latus rectum is equal to its

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NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 13 - Ellipse>Exercise 1>Q 18

If the eccentricity of the two ellipse

\frac{x^{2}}{169} + \frac{y^{2}}{25} = 1

and

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

are equal, then the value of

\frac{a}{b}

is

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NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 13 - Ellipse>Exercise 1>Q 19

The length of the latus rectum of an ellipse is

\frac{1}{3}

of the major axis. Its eccentricity is

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 13 - Ellipse>Exercise 1>Q 20

If

P \equiv (x, y), F_{1} \equiv (3, 0), F_{2} \equiv (- 3, 0)

and

16 x^{2} + 25 y^{2} = 400

, then

P F_{1} + P F_{2}

equals

HARD

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 13 - Ellipse>Exercise 1>Q 21

For what value of

λ

does the line

y = x + λ

touches the ellipse

9 x^{2} + 16 y^{2} = 144

.

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NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 13 - Ellipse>Exercise 1>Q 22

If

(\sqrt{3}) b x + a y = 2 a b

touches the ellipse

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

then the eccentric angle of the point of contact is