Question

In parabola $y^2=18x$ find the point where the ordinate is equal to three times the abscissa.

Answer 1

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

Now since the point lies on the parabola $y^2=18x$.

Therefore,

${\left(3a\right)}^2=18\cdot a$

$9a^2=18a$

$\Rightarrow a=2$

Hence the required point is $(2,6)$.