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Question:
at what point of the parabola x to the power 2=9y is the abscissa three times that of ordinate
Answer:

Given, parabola is x2 = 9y

Let P(h, k) is the point on the parabola such that abscissa is 3 times the ordinate.

So, h = 3k   .........1

Since P(h, k) lies on the parabola

So, h2 = 9k .........2

From equation 1 and 2, we get

    (3k)2 = 9k

=> 9k2 = 9k

=> 9k2 - 9k = 0

=> 9k(k - 1) = 0

=> k = 0, 1

When k = 0, h = 0

So k = 1

Now, from equation 1,

h = 3 * 1 = 3

So, the point is (3, 1)

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