question_answer

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

Correct Answer: A

Solution :

Given hyperbola is

\[\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\]

Satisfying the point (4, 2)

\[\Rightarrow \]   \[{{b}^{2}}=\frac{4}{3}\]

\[\Rightarrow \]   \[e=\frac{2}{\sqrt{3}}.\]