5: In order to intersect itself at two different times t and
s, the equality
x(t) = x(s)
would have to be true, which yields
s = −t. But then
y(s) = −y(t) ≠ y(t).
The y-coordinates cannot
agree as they are never zero, so the opposite sign means that they are
different. Thus no intersection is possible.
Thus the length is
![](gif7/ecd7ae2.gif)
Simplify the polynomial under the root.
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Answer