If the latus rectum of an ellipse be equal to half of its mi... | MATH - ELLIPSE | SolveeIt | Solveeit

Today, August 18

Question

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

A

$\frac{3}{2}$

B

$\frac{\sqrt{3}}{2}$

C

$\frac{2}{3}$

D

$\frac{\sqrt{2}}{3}$

Answer

$\frac{\sqrt{3}}{2}$

Explanation

Solution

given $\frac{2b^{2}}{a} = \frac{1}{2}(2b)$ Ž 2b = a Ž 4b² = a²

Ž 4a²(1 – e²) = a² Ž 4 – 4e² = 1 Ž e² = 3/4

Ž e = $\frac{\sqrt{3}}{2}$