Question

Assertion :The points of contact of the vertical tangents to $x=5-3\cos \theta$, $y=3+5\sin \theta$ are $(2,3)$ & $(8,3)$. Reason: For vertical tangent $\frac{dx}{d\theta }=0$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

For vertical tangent $\frac{dx}{d\theta }=0$
$\therefore$ $3\sin \theta =0$ $\Rightarrow$ $\theta =0,\pi$
at $\theta =0$, $x=5-3\left(1\right)=2$
& $Y=3+0=3$
$\therefore$ When $\theta =0$, point of contact of vertical tangent $=(2,3)$ and for $\theta =\pi ,(x,y)=(8,3)$