Parametric Equations (Calc.2)

1. Apr 1, 2013

dolpho

1. The problem statement, all variables and given/known data

Parametrize the curve by a pair of differentiable functions x = x(t), y = y(t) with [x '(t)]2 + [y '(t)]2≠0, then determine the tangent line at the origin.

y=2x^3

3. The attempt at a solution

Honestly I don't really understand what it's asking for. I assume it wants us to make 2 equations, x= something and y = something but I'm not quite sure how to get there. Then we can find the tangent line by taking the derivative.

Unfortunately I can't even show work on this problem since I don't even know where to start. Would appreciate any help on this question <3

2. Apr 1, 2013

HallsofIvy

"Parametric equations" for a curve in the xy-plane are two equation x= f(t), y= g(t) such that, for any t, the corresponding point (x(t), y(t)) is a point on the curve. In particular, if the curve is given a function, y= F(x), we can just write x= t, y= F(t).

3. Apr 1, 2013

dolpho

Hmmmm right... So I'm a bit confused on how we take our starting equation and turn it into two.

Would we just do

y=2x^3 and x = (y/2)^1/3 ?

4. Apr 1, 2013

dolpho

Hmmmm right... So I'm a bit confused on how we take our starting equation and turn it into two.

Would we just do

y=2t^3 and x = (t/2)^1/3 ?

5. Apr 1, 2013

Staff: Mentor

No. Here you are apparently finding the inverse of the function. The first equation has y as a function of x, and the second has x as a function of y.

Your first equation can be symbolized as y = f(x), and the second as x = f-1(y).
That's not what you need to do.

No. How about x = t? What would y be then, as a function of t?