Question

A point on the parabola $y^2=18x$ at which the ordinate increase at twice the rate of the abscissa is _______, $(\frac{dx}{dt}\ne 0)$.

• 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 $(\frac{9}{8},\frac{9}{2})$

Ordinate increases at twice the rate of abscissa means

$dy=2dx$

$⟹\frac{dy}{dx}=2$

Now,

$y^2=18x$

$⟹2y\frac{dy}{dx}=18$

$⟹2y\times 2=18$

$⟹y=\frac{9}{2}$

Now, $x=\frac{y^2}{18}=\frac{81}{4\times 18}=\frac{9}{8}$

The point is $(\frac{9}{8},\frac{9}{2})$