Question

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

• A. $(2,4)$
• B. $(4,3)$
• C. $(-4,3)$
• D. $(-4,-3)$

Answer 1

The correct option is A $(2,4)$

According to question,

Rate of change of Abscissa = rate of change of ordinate

$\Rightarrow dx=dy$ ---------$\left(1\right)$

equation , $y²=8x$

differentiate with respect to $x$

$2y.dy/dx=8$

$2ydy=8dx$

from equation $\left(1\right)$

$2y=8\Rightarrow y=4$ , now put it in equation of curve

$y²=8x$

$\Rightarrow \left(4\right)²=8x$

$\Rightarrow 16=8x\Rightarrow x=2$

Hence, point on the curve is $(2,4)$