Question

Find the locus of P, if for all values of α, the co-ordinates of a moving point P is (9 cos α, 9 sin α)

Answer 1

Let P(h, k) be the moving point.

We are given h = 9 cos α and k = 9 sin α and

⇒ cos α = `"h"/9` and sin α = `"k"/9`

We know cos²α + sin²α = 1

⇒ `("h"/9)^2 + ("k"/9)^2` = 1

(i.e.) `"h"^2/81 + "k"^2/81` = 1

⇒ h² + k² = 81

∴ Locus of the point is x² + y² = 81