Let $F_1$ and $F_2$ be the two foci of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ with $a \gt b \gt 0$. If the latus rectum through $F_1$ subtends $90^{\circ}$ at $F_2$ then the eccentricity of the ellipse is

• A

  $3-2 \sqrt{2}$
• Correct answer
  B

  $\sqrt{2}-1$
• C

  $2 \sqrt{2}-2$
• D

  $\frac{1}{\sqrt{2}}$

Hence, the correct answer is option: 'B'.