Q. A point on the parabola $y^{2} = 18x$ at which the ordinate increases at twice the rate of the abscissa, is
A) (2,4)
B) (2,-4)
C) $\left( - \frac{9}{8},\frac{\ \ 9}{2} \right)$
D) $\left( \frac{9}{8},\frac{9}{\ 2} \right)\ \ \$
Explanation
(d)
Equation of parabola is $y^{2} = 18x$….(i)
$\Rightarrow \ 2y\frac{dy}{dt} = 18\frac{dx}{dt} \Rightarrow 2.2y = 18\ \ \ \ \ \ \ \ \left\lbrack \therefore\frac{dy}{dt} = 2\frac{dx}{dt} \right\rbrack$
$\Rightarrow \ \ y = \frac{9}{2}\$
$\therefore\ \ From\ Eq.(i),\left( \frac{9}{2} \right)^{2} = 18x \Rightarrow x = \frac{9}{8}$
$\therefore Point\ is\left( \frac{9}{8},\frac{9}{2} \right).$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.