Question

Find the locus of P, if for all values of α, the co-ordinates of a moving point P is (9 cos α, 6 sin α)

Answer 1

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

We are given h = 9 cos α and k = 6 sin α

⇒ cos α = `"h"/9` and sin α = `"k"/6`

cos²α + sin²α = 1

⇒ `("h"/9)^2 + ("k"/6)^2` = 1

∴ `"h"^2/81 + "k"^2/36` = 1

∴ Locus of the point is `x^2/81 + y^2/36` = 1