Question

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

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

Answer 1

Answer: (A)

$\frac{2}{\sqrt{3}}$

Answer 2

$\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$
$2a =4 a=2$
$\frac{x^{2}}{4} - \frac{y^{2}}{b^{2}} = 1$
Passes through $(4,2)$
$4 - \frac{4}{b^{2}} = 1 \Rightarrow b^{2} = \frac{4}{3} \Rightarrow e = \frac{2}{\sqrt{3}}$