Re: Point of intersection

On Mon, 31 Mar 2008 00:24:22 EDT, *** <cheney4prez2008@xxxxxxxxx>
wrote:

The parametric equations traces out a loop

x = 5 - (3/2)t^2

y = -(1/2)t^3 + 3t +2

What are the values of t at which the curve intersects itself?

Suppose (x(t),y(t)) = (x(s),y(s)).

Leave s,t unknown, and set up 2 algebraic equations:

x(t) = x(s)
y(t) = y(s)

Thus, 2 equations, 2 unknowns.

The rest is elementary algebra -- I'm sure you're up to it.

Note -- since you want s =/= t, you can assume s - t is nonzero. Thus,
if you get an equation with 0 on one side, and a factor of s - t on
the other, you can divide out that factor.

quasi
.