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

(2, 4)

The correct answer is Option (2) → (2, 4)

$y^2 = 8x$

$\frac{dy}{dx}$ is required.

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

$\frac{dy}{dx} = \frac{4}{y}$

Equal rate of change of abscissa and ordinate means:

$\frac{dy}{dx} = \pm 1$

Case 1: $\frac{4}{y}=1 \Rightarrow y=4$

$x=\frac{y^2}{8}=\frac{16}{8}=2$

Case 2: $\frac{4}{y}=-1 \Rightarrow y=-4$

$x=\frac{16}{8}=2$

The points where abscissa and ordinate change at the same rate are $(2,4)$ and $(2,-4)$.