Question

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

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

Answer 1

Answer: (B)

$\sqrt{3}$

$\begin{array}{c}Focusoftheellipse\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\\ willbe\left(\pm \sqrt{a^2-b^2},0\right)\\ Ifthehyperbolapassesthroughthefocusofellipsethen\\ \frac{\left(\pm \sqrt{a^2-b^2}\right)h^2}{b^2}-0=1\\ a^2-b^2=b^2\\ \left[a^2=2b^2\right]\\ Eccentricityofthegivenhyperbolacanbegivenas\\ e=\sqrt{1+{\left(\frac{a}{b}\right)}^2}\\ =\sqrt{1+2}\\ \left[e=\sqrt{3}\right]\end{array}$