If eccentricity of an ellipse be 1/√ 2 , then its latus rectum is equal to its

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10-2. Parabola, Ellipse, Hyperbola

easy

If the eccentricity of an ellipse be $1/\sqrt 2 $, then its latus rectum is equal to its

A

Minor axis

B

Semi-minor axis

C

Major axis

D

Semi-major axis

Solution

(d) $e = \frac{1}{{\sqrt 2 }}$;

Latus rectum $ = \frac{{2{b^2}}}{a} = \frac{{2{a^2}}}{a}\left( {1 – \frac{1}{2}} \right) = a$
$i.e.$, semi-major axis.

Standard 11

Mathematics

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