Question

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

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

Answer 1

Answer: (A)

$(\frac{9}{8},\frac{9}{2})$

Given, $y^2=18x$
On differentiating on both sides w.r.t $t$ we get
$2y\left(\frac{dy}{dt}\right)=18\left(\frac{dx}{dt}\right)$
$\Rightarrow 2y\left(2\frac{dx}{dt}\right)=18\left(\frac{dx}{dt}\right)(\because \frac{dy}{dt}=2\frac{dx}{dt})$
$\Rightarrow 4y=18$
$\Rightarrow y=\frac{9}{2};x=\frac{y^2}{18}=\frac{9}{8}$
Hence the required point is $(\frac{9}{8},\frac{9}{2})$