Question

The difference between the length $2a$ of the transverse axis of a hyperbola of eccentricity $e$ and the length of its latus rectum is :

• A. $2a|3-e^2|$
• B. $2a|2-e^2|$
• C. $2a(e^2-1)$
• D. $a(2e^2-1)$

Answer 1

Answer: (B)

$2a|2-e^2|$

Let the equation of hyperbola be $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

Length of transverse axis is $2a$ and

Length of latus rectum is $\frac{2b^2}{a}$

Now, difference $=|2a-\frac{2b^2}{a}|=\frac{2}{a}|2a^2-a^2{e}^2|$

$\therefore$ Difference $=2a|2-e^2|$