Hyperbola

61. Assertion (A) The distance between the points $p\left(\frac{\pi}{4}\right)$ and $p\left(\frac{\pi}{3}\right)$ on the hyperbola $9 x^2+16 y^2=9$ is

\(\frac{1}{2 \sqrt{2}} \sqrt{66-33 \sqrt{2}-9 \sqrt{3}}\)

Reason (R) $x=a \cosh t, y=b \sinh t$ are the parametric equations of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

The correct option among the following is