Question

Let the foci of the hyperbola $\frac{x^2}{A^2}-\frac{y^2}{B^2}=1$ be the vertices of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and the foci of the ellipse be the vertices of the hyperbola. Let the eccentricities of the ellipse and hyperbola be $e_1$ and $e_2$ respectively. Given $b=1$ and $e_2=2$.
The length of the latus-rectum of the hyperbola is equal to

• A. $\frac{1}{\sqrt{3}}$
• B. $\frac{2}{\sqrt{3}}$
• C. $\sqrt{3}$
• D. $2\sqrt{3}$

Answer 1

Answer: (D)

$l$ (latus rectum of hyperbola) $=\frac{2B^2}{A}=2\sqrt{3}$.