At what point of the parabola x2=9y is the abscissa three times that of ordinate ?

pls answer it as soon as possible.

The given parabola is x2 = 9y.

Let P(h, k) be the point on the parabola such that abscissa is three times the ordinate.

h = 3k    ...(1)

P(h, k) lies on the parabola x2 = 9y,

h2 = 9k   ...(2)

From (1) and (2), we have

(3k)2 = 9k

∴ 9k2 – 9k = 0

⇒ 9k (k – 1) = 0

k = 0 or k – 1 = 0

k = 0 or k = 1

k = 1                (When k = 0, h = 0)

When k = 1, we get

h = 3 × 1 = 3           (Using (1))

Thus, the required point is (3, 1). 

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