Question

The point of contact of vertical tangent to the curve given by the equations $x=3-2\cos \theta ,y=2+3\sin \theta$ is

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

Answer 1

Answer: (B), (C)

(1, 2)
(5, 2)

$x=3-2cos\theta ,y=2+3sin\theta$
The slope of the tangent at ${}^{\prime }{\theta }^{\prime }$ is $\frac{dy}{dx}=\frac{\frac{dy}{d\theta }}{\frac{dx}{d\theta }}$
$\therefore$ for vertical tangent $\frac{dx}{d\theta }=0i.e.,2sin\theta =0$
$\Rightarrow \theta =0$ or $\pi or2\pi$
Then $x=1,y=2;x=5,y=2;x=1,y=2$
$\therefore$ the points of contact are $(1,2),(5,2)$