Question

The points of contact of the vertical tangents to $x=2-3\sin \theta ,y=3+2\cos \theta$ are

• A. (2,5),(2,1)
• B. (-1,3),(5,3)
• C. (2,5),(5,3)
• D. (-1,3), (2,1)

Answer 1

Answer: (B)

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 $(5,3)$