Question

The transverse axis of a hyperbola is double the conjugate axes. Whats the eccentricity of the hyperbola

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

A hyperbola is given by,

Transverce axis = AB = 2a

conjugate axis = CD 2b

These lengths are related to the eccentricity of the hyperbola by the relation,

$b^2=a^2(e^2-1)$.

$b^2=4b^2(e^2-1)$

i.e.,$e^2-1=\frac{1}{4}$

$e^2=\frac{5}{4}$

$e=\frac{\sqrt{5}}{4}$