Question

The points of contact of the vertical tangents to

x = 2 – 3 sin θ, y = 3 + 2 cos θ 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 –3cos θ = 0

⇒ = $\frac{\pi}{2}$ or $\frac{3\pi}{2}$. Corresponding to these values of θ, 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).