Question

For what point of the parabola $y^2=18x$ is the ordinate equal to three times abscissa.

Answer 1

Let us assume that point $P$ has abscissa $a$. Hence, the ordinate of point $P$ is $3a$.

Now, as $P$ lies on $y^2=18x$, substitute $P$ in the equation of the parabola to find the value of $a$.

$⟹(3a{)}^2=18a$

$⟹9a^2=18a$

$⟹a^2=2a$

$⟹a=2$ or $a=0$

If $a=0$ then, the abscissa and ordinate of $P$ become the same and hence cannot be true according to given condition.

Hence, $a=2$ and the coordinates of required point are $(2,6)$.