Question

A hyperbola has its centre at the origin, passes through the point $(4,2)$ and has transverse axis of length $4$ unit along the $x-$axis. Then the eccentricity of the hyperbola is

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

Answer 1

The correct option is B $\frac{2}{\sqrt{3}}$

Given $2a=4$
$\Rightarrow a=2$
The hyperbola
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
passes through $(4,2)$
So, $\frac{4^2}{2^2}-\frac{2^2}{b^2}=1$
$\Rightarrow b^2=\frac{4}{3}$
$\therefore e=\sqrt{1+\frac{b^2}{a^2}}=\frac{2}{\sqrt{3}}$