At what point of the parabola x 2 = 9y is the abscissa three times that of ordinate?

Question

Philoid · Accepted Answer

Given that we need to find the point on parabola x² = 9y such that the abscissa is three times the ordinate.

Let us assume the point be (3y₁, y₁). Substituting in the parabola we get,

⇒ (3y₁)² = 9(y₁)

⇒ 9y₁² = 9y₁

⇒ y₁² - y₁ = 0

⇒ y₁(y₁ - 1) = 0

⇒ y₁ = 0 or y₁ - 1 = 0

⇒ y₁ = 0 or y₁ = 1

The points is B(3(1), 1) i.e, (3, 1).

∴The point is (3, 1).