The point on the curve $y^2 = 8x$ for which the abscissa and ordinate change at the same rate, is
Answer & explanation
Correct answer: option 2
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 $(2,-4)$.