A point on the parabola $y^2=18 x$ at which the ordinate increases at twice the rate of the abscissa, is

$(9 / 8,9 / 2)$

We have,

$ y^2=18 x $

$\Rightarrow 2 y \frac{d y}{d t}=18 \frac{d x}{d t}$

$\Rightarrow 2 y \times 2 \frac{d x}{d t}=18 \frac{d x}{d t}$              $\left[∵ \frac{d y}{d t}=2 \frac{d x}{d t}\right]$

$\Rightarrow 4 y=18 \Rightarrow y=\frac{9}{2}$

When $y=\frac{9}{2}$, we have

$\left(\frac{9}{2}\right)^2=18 x \Rightarrow x=\frac{9}{8}$

Hence, the required point is $(9 / 8,9 / 2)$