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JEE Previous Year Question

$If the latus rectum of an ellipse is equal to half of minor axis, then its eccentricity is$

Topic: JEE PYQ

Answer: D. Full step-by-step solution below.

A $\frac{3}{4}$
B $\frac{3}{4}$
C $\frac{1}{4}$
D $\frac{3}{2}$

Correct answer: D

Solution

(d) Let the equation of ellipse be \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1 ∴ Length of Latus rectum = \frac{2 b ^{2}}{a} and length of minor axis = 2 b ∴ \frac{2 b ^{2}}{a} = b \Rightarrow \frac{b ^{2}}{a ^{2}} = \frac{1}{4} e = 1 - \frac{b ^{2}}{a ^{2}} = 1 - \frac{1}{4} = \frac{3}{2}

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