Question

The points of contact of the vertical tangents to x = 2–3 sin q, y = 3 + 2 cos q 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)

(–1, 3), (5, 3)

Answer 2

For vertical tangents $\frac{dx}{d\theta}$= 0 so, we have –3 cos q = 0

Ž q = $\frac{\pi}{2}$or $\frac{3\pi}{2}$. Corresponding to these values of q,

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), (5, 3)