A point on the parabola $y^2=18 x$ at which the ordinate increases at twice the rate of the abscissa, is
Answer & explanation
Correct answer: option 1
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 $(9 / 8,9 / 2)$