Question

If latus rectum of hyperbola subtends a right angle at the other focus, then the eccentricity of hyperbola is

• A. $2\sqrt{2}-1$
• B. $\sqrt{2}+2$
• C. $\sqrt{2}+1$
• D. $1+2\sqrt{2}$

Answer 1

The correct option is C $\sqrt{2}+1$

$\tan 45°=\frac{LS}{S{S}^{\prime }}=1$
$\Rightarrow LS=S{S}^{\prime }$
$\Rightarrow \frac{b^2}{a}=2ae$
$\therefore \frac{a^2(e^2-1)}{a}=2ae$
$\Rightarrow e^2-2e-1=0$
$\Rightarrow (e-1{)}^2=2$
$\Rightarrow e=1+\sqrt{2}$