Question

Given the equations x=t^3-6t and y=t^2 how would you find the point where the curve crosses itself?

Answer 1

set \(x=y\) ?

Answer 2

\((0,0)\)is one such point by inspection, if \(t=0\)

Answer 3

otherwise solve
\[t^3-6t=t^2\] for \(t\)

Answer 4

I dont belive it crosses itself at (0,0)

Answer 5

put \(t=0\) and you will see that it does

Answer 6

http://www.wolframalpha.com/input/?i=x%3Dt^3-6t%2Cy%3Dt^2+