point on the parabola y² = 18x at which the ordinate increases at twice the rate of abscissa is :

Given  $\frac{dy}{dt}=2\frac{dx}{dt}$$\Rightarrow$ $\frac{dy}{dx}=2$

  from the parabola $2y\frac{dy}{dx}=18$ $\Rightarrow$ $2y=9\Rightarrow y=\frac{9}{2}$ and $x=\frac{1}{18}{y}^2=\frac{1}{18}\cdot \frac{9}{2}\cdot \frac{9}{2}=\frac{9}{8}$

$\therefore$ Required point is $\left(\frac{9}{8},\frac{9}{2}\right)$