Question

The eccentricity of the ellipse whose latus rectum is equal to $\frac{3}{2}$ (half of its minor axis) is

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$\frac{2b^2}{a}=\frac{3}{2}b\Rightarrow 4b=3a\Rightarrow 16b^2=9a^2\Rightarrow (1-e^2)=\frac{9}{16}\Rightarrow e^2=\frac{7}{16}\Rightarrow e=\frac{\sqrt{7}}{4}$