A particle moves along the curve x² = 2y. At what point, ordinate increases at the same rate as abscissa increases?

Given: A particle moves along the curve x² = 2y.

To Find: The point where ordinate increases at the same rate as abscissa increases.

Let, the point is (x, y), at which the ordinate increases at same rate as abscissa increases, i.e., .

Given curve is, x² = 2y

Differentiating with respect to t we get,

⇒

⇒ 2x = 2 [as ]

⇒ x = 1

Putting x = 1 in the equation of curve we get,

⇒ 1 = 2y

⇒ y =

So, the point is (1, ).