The standard parametric representation of a parabola is with

MATHEMATICS · Multi-part · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

The standard parametric representation of a parabola is

x = 2at^{2},\,y = 2at

with

a>0

. Let

a=3

. (a) Find

\dfrac{dy}{dx}

in terms of

t

. (b) Determine the value(s) of

t

for which the slope of the tangent is

-\dfrac{1}{2}

. (c) Write the Cartesian equation of each tangent obtained in part (b).