If $P,Q,R$ are three points on the ellipse $\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}+\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1$whose eccentric angles are $\mathrm{\theta },\mathrm{\theta }+\mathrm{\alpha },\mathrm{\theta }+2\mathrm{\alpha }$, then mark the correct option(s).

The area of $\mathrm{\Delta PQR}$ is independent of $\text{'}\mathrm{\alpha }\text{'}$

The area of $\mathrm{\Delta PQR}$ is minimum when $\mathrm{\alpha }=\frac{2\mathrm{\pi }}{3}$

When $\mathrm{\alpha }=\frac{\mathrm{\pi }}{2}, \mathrm{\theta }=\frac{\mathrm{\pi }}{4}$ then area $\mathrm{\Delta PQR}$ is 'ab' sq.units

The area of $\mathrm{\Delta PQR}$ when $\mathrm{\theta }=\frac{\mathrm{\pi }}{6}\mathrm{is} \frac{\sqrt{3}}{2}$time area of $\mathrm{\Delta PQR}$ when  $\mathrm{\theta }=\frac{\mathrm{\pi }}{3}$