Question

A point is moving along the curve $y^3=27x$ The interval in which the abscissa changes at slower rate than ordinate is

• A. $(-3,3)$
• B. $(-\infty ,\infty )$
• C. $(-1,1)$
• D. $(-\infty ,-3)(3,\infty )$

Answer 1

Answer: (C)

$(-1,1)$

$\left|\frac{dx}{dt}\right|<\left|\frac{dy}{dt}\right|$
$\therefore \left|\frac{dy}{dx}\right|>1$
Now $3y^2\frac{dy}{dx}=27\Rightarrow \frac{dy}{dx}=\frac{9}{y^2}$
$\therefore \frac{9}{y^2}>1\Rightarrow y^2<9$
$\Rightarrow -3<y<3\Rightarrow -27<y^3<27$
$\Rightarrow -27<27x<27\Rightarrow -1<x<1$