Question

Let the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be reciprocal to that of the ellipse $x^2+9y^2=9$, then the ratio $a^2:b^2$ equals

• A. $8:1$
• B. $1:8$
• C. $9:1$
• D. $1:9$

Answer 1

The correct option is A $8:1$

Eccentricity of ellipse $e=\sqrt{1-\frac{1}{9}}=\sqrt{\frac{8}{9}}$
Eccentricity of hyperbola $=\sqrt{\frac{9}{8}}$
$\Rightarrow 1+\frac{b^2}{a^2}=\frac{9}{8}$
$\Rightarrow \frac{b^2}{a^2}=\frac{1}{8}$