Question

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

Answer 1

Let the required point be $(3a,a)$.

Now since the point lies on the parabola $x^2=9y$.

Therefore,

${\left(3a\right)}^2=9\cdot a$

$9a^2=9a$

$\Rightarrow a=1$

Hence the required point is $(3,1)$.