Question

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

• A. $(\frac{9}{8},\frac{9}{2})$
• B. $(2,-4)$
• C. $(-\frac{9}{8},\frac{9}{2})$
• D. $(2,4)$

Answer 1

The correct option is A $(\frac{9}{8},\frac{9}{2})$

$y^2=18x\Rightarrow 2y\frac{dy}{dx}=18\Rightarrow \frac{dy}{dx}=\frac{9}{y}$
$Given\frac{dy}{dx}=2\Rightarrow \frac{9}{y}=2\Rightarrow y=\frac{9}{2}$
Putting in $y^2=18x\Rightarrow x=\frac{9}{8}$
$\therefore$ Required point is $(\frac{9}{8},\frac{9}{2})$