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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)
Solution
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
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