If $\mathrm{P}\left(\frac{\pi }{3}\right)\text{ and }\mathrm{Q}\left(\frac{2\pi }{3}\right)$ represents two points on the circle $x^2+y^2-4x+6y-12=0$ in parametric form, then the length of the chord PQ is

$x^2+y^2-4x+6y-12=0$

radius(r)=5

Parametric point of the circle is

$=\left(x_1\pm r\cos \theta ,y_1\pm \sin \theta \right)$

$P=\left(2+5\cos \frac{\pi }{3},-3+5\sin \frac{\pi }{3}\right)$ and $Q=\left(2+5\cos \frac{2\pi }{3},-3+5\sin \frac{2\pi }{3}\right)$

$P=\left(\frac{9}{2},\frac{5\sqrt{3}-6}{2}\right)$ and $Q=\left(\frac{-1}{2},\frac{5\sqrt{3}-6}{2}\right)$ then

length of the chord PQ is

$PQ=5$