Question

The points on the curve $12y=x^3$ whose ordinate and abscissa change at the same rate, are

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

Answer 1

The correct option is A $(-2,-2/3),(2,2/3)$

Given, $\frac{dy}{dt}=\frac{dx}{dt}$

Given equation of curve is $12y=x^3$

$\Rightarrow 12\frac{dy}{dt}=3x^2\frac{dx}{dt}$

$\Rightarrow (12-3x^2)\frac{dy}{dt}=0$

$\Rightarrow x=\pm 2$

$\Rightarrow y=\pm \frac{2}{3}$

Hence, the points are $(2,\frac{2}{3}),(-2,-\frac{2}{3})$