Question

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. $\left(\frac{9}{8}, \frac{9}{2}\right)$

Answer 1

Answer: (D)

Any point be $\left( \frac{9}{2} t^{2}, 9t \right) ;$ differentiating $y^2 = 18x$
$\Rightarrow \frac{dy}{dx} = \frac{9}{y} = \frac{1}{t} = 2$ (given) $\Rightarrow t = \frac{1}{2}$
$\Rightarrow $ Point is $\left(\frac{9}{8}, \frac{9}{2}\right)$