Hello, 1sttime!
Graph each of the following sets of parametric equations
by eliminating the parameter to get a cartesian equation.
Explain the difference between how the two parametric curves are traced out.
. .
We have: .
Hence: .
This is a hyperbola. Code:

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With the cartesian equation, we trace the curve as goes from to
The curve goes from to , forming the left branch.
The function is undefined at
Then the curve goes from to , forming the right branch.
With the parametric equations, we trace the curve as goes from to .
When , we have: . . . . the point
When , we have: . . . . the point
. . Hence, as goes from to , the right branch is traced out.
And we find that, as goes from to , the left branch is traced out.
And that is the difference in the tracing of the two equivalent functions.