If the circle whose diameter is the major axis of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \left(a>b>0\right)$ meets the minor axis at point $P$ and the orthocentre of $∆P{F}_1{F}_2$ lies on the ellipse, where $F_1$ and $F_2$ are the foci of the ellipse, then the square of the eccentricity of the ellipse is

• Correct answer
  A

  $\frac{\sqrt{5}-1}{2}$
• B

  $\sqrt{3}-1$
• C

  $\frac{1}{\sqrt{2}}$
• D

  $\frac{\sqrt{3}}{2}$

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