Thank you for reporting, we will resolve it shortly
Q.
The points of contact of the vertical tangents to $x=2-3 \,\sin \theta, y=3+2\,\cos\, \theta$ are
Application of Derivatives
Solution:
For vertical tangents $\frac{dx}{d \theta}=0$ so, we have
$-3 \cos \,\theta=0 \Rightarrow \theta=\frac{\pi}{2}$ or $\frac{3 \pi}{2}$
Corresponding to these values of $\theta$, we have
$x=2-3\,\sin \,\frac{\pi}{2}=-1$
$y=3+2 \,\cos \,\frac{\pi}{2}=3$;
$x=2-3 \,\sin\, \frac{3 \pi}{2}=2+3=5$,
$y=3+2 \,\cos \frac{3 \pi}{2}=3$
Thus, the required points are $(-1, 3)$ and $(5, 3)$