Question

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

Answer 1

hope this helps you

Answer 2

The point on the parabola is (9/8, 9/2)

• Given,

       Rate of change of y = 2(Rate of change of x)

                  $\frac{dy}{dt} = 2\frac{dx}{dt}$

                  $(\frac{dy}{dt} )/(\frac{dx}{dt} )$ = 2

                  $\frac{dy}{dx}$ = 2   --------------------------(1)

• Given parabola,

                  $y^{2}$ = 18x  ------------------------(2)

• Differentiating on both sides with respect to x

                  $2y\frac{dy}{dx}$ = 18(1)

                   y(2) = 9                                [ from (1)]

                   y = 9/2

• Substituting y in (2), we get

                  (9/2)^2 = 18x

                   81/4 = 18x

                     x = 9/8