Given: a point on the curve y² = 8x.

To find the point on the curve at which the abscissa and ordinate change at the same rate

Equation of curve is y² = 8x

Differentiating the above equation with respect to t, we get

When abscissa and ordinate change at the same rate, i.e.,

Equating equation (i) and equation (ii), we get

⇒ y = 4

When y, y² = 8x ⇒ (4)² = 8x ⇒ x = 2

Hence the point on the curve at which the abscissa and ordinate change at the same rate is (2,4)