Find the point on the curve `y^2dot` `8xdot` for which the abscissa and ordinate change at the same rate.

Explanation

`y^{2}=8 x ldots(1) `


`Rightarrow 2 y frac{d y}{d t}=8 frac{d x}{d t} `


`Rightarrow 2 y=8[because frac{d y}{d t}=frac{d x}{d t}] `


`Rightarrow y=4 `


`Rightarrow x=frac{y^{2}}{8}[text { From eq } cdot(1)] `


`Rightarrow x=frac{16}{8}=2`



So, the point is `(2,4)`.