Question

A point on the parabola $y^2=18x$ at which the ordinate increase at twice the rate of the abscissa is

• A. $(9/8,9/2)$
• B. $(2,-4)$
• C. $(-9/8,9/2)$
• D. $(2,4)$

Answer 1

The correct option is A $(9/8,9/2)$

Given $\frac{dy}{dt}=2\frac{dx}{dt}$

Given, $y^2=18x$

$2y\frac{dy}{dt}=18\frac{dx}{dt}$

$\Rightarrow 4y\frac{dx}{dt}-18\frac{dx}{dt}=0$

$\Rightarrow 4y-18=0$ [since $\frac{dx}{dt}\ne 0$]

$\Rightarrow y=\frac{9}{2}$

$\Rightarrow x=\frac{9}{8}$

Hence, the required point is $(\frac{9}{8},\frac{9}{2})$