Find a point on the curve `y^(2)=2x` at which the abscissa and ordinates are increasing at the same rate.

Explanation

Let the required point be (x, y).
`y^(2) = 2x" "….(1)`
`rArr 2y(dy)/(dt) = 2 . (dx)/(dt)`
`"But" (dy)/(dt)=(dx)/(dt)`
`:." "2y(dx)/(dt) = 2 (dx)/(dt)`
`rArr " "2y = 2`
` rArr " "y = 1`
From (1)
`2x= (1)^(2) rArr x= 1//2`
`:. ` Required point = (1/2, 1).