Question

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

Answer 1

Putting x = 3y in the given equation of the parabola:
$$\begin{gathered} 9y^2=9y \\ \Rightarrow 9y\left(y-1\right)=0 \\ \Rightarrow y=0,1 \end{gathered}$$

At y = 0, x = 0
At y = 1, x = 3

Therefore, at (1, 3), the abscissa is three times that of the ordinate.