Question

If hyperbola $\frac{x^2}{b^2}-\frac{y^2}{a^2}=1$ passes through the focus of ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ then eccentricity of hyperbola is.

• A. $\sqrt{3}$
• B. $\sqrt{2}$
• C. $\sqrt{5}$
• D. 2

Answer 1

Answer: (A)

$\frac{x^2}{b^2}-\frac{y^2}{a^2}=1$ passes through $(\pm ae,0)$
$\therefore \frac{a^2{e}^2}{b^2}=1$
$\therefore e^2=\frac{b^2}{a^2}$
$1-\frac{b^2}{a^2}=\frac{b^2}{a^2}$
$\therefore \frac{b^2}{a^2}=\frac{1}{2}$
$\therefore e_H=\sqrt{1+\frac{a^2}{b^2}}=\sqrt{3}$