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Question: If the latusrectum of an ellipse be equal to one half of its minor axis, the eccentricity of the ell...

If the latusrectum of an ellipse be equal to one half of its minor axis, the eccentricity of the ellipse is

A

14\frac{1}{4}

B

12\frac{1}{2}

C

32\frac{\sqrt{3}}{2}

D

23\frac{2}{\sqrt{3}}

Answer

32\frac{\sqrt{3}}{2}

Explanation

Solution

Given 2b2a=12(2b)\frac{2b^{2}}{a} = \frac{1}{2}(2b) ⇒ 2b = a

⇒ 4b2 = a2

⇒ 4a2 (1 – e2) = a2

⇒ e = 32\frac{\sqrt{3}}{2}