Question

The eccentricity of the hyperbola $x^{2}-3y^{2}-2x-8=0$ is

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

Answer 1

Answer: (C)

The given equation reduces to $\frac{(x-1)^2}{9}-\frac{y^2}{3}$ $=1$.
Thus, $a^2=9, b^2=3$
Using $b^2=a^2 e^2-1$, we get
$3=9 e^2-1$
$\Rightarrow e=\frac{2}{\sqrt{3}}$