Question

Find the point on the curve $y^2=8x$ for which the abscissa and ordinate change at the same rate.

Answer 1

Let the required point be (x,y).

Given,

$\frac{dy}{dt}=\frac{dx}{dt}$ .......(1)

And, $y^2=8x$ ......(1)

On differentiating both sides of equation 2 w.r.t. t, we get,

$2y\frac{dy}{dt}=8.\frac{dx}{dt}$

$2y=8$

$y=4$

On putting $y=4$ in equation 2, we get,

$8x=16⟹x=2$

Hence, the required point is $(2,4)$.