Question

The eccentricity of a standard hyperbola passing through the points $(3,0),(3\sqrt{2},2)$ will be

• A. $\sqrt{13}$
• B. $\frac{\sqrt{13}}{3}$
• C. $\frac{\sqrt{13}}{4}$
• D. $\frac{\sqrt{13}}{2}$

Answer 1

Answer: (B)

$\frac{\sqrt{13}}{3}$

Equation of hyperbola is $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

At $(3,0)$, $\frac{9}{a^2}=1$

$\Rightarrow a=3$

At $(3\sqrt{2},2),\frac{18}{a^2}-\frac{4}{b^2}=1$
$\Rightarrow b^2=4$
$\therefore e=\sqrt{1+\frac{4}{9}}=\frac{\sqrt{13}}{3}$