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).