I have a parametrization for a curve..

Question

x = 5 cos t
y = 2 sin t

I made the graph...
its initial point is (3,0), and curves up and to the left.

So, I have my points for the graph. How do I come up with the cartesian equation?

Answer 1

(x/5)^2 + (y/2)^2 = 1
is the Cartesian form.

This is the equation of an ellipse centered at the origin.

(3,0) cannot be on the curve, because when y=0, t = 0 or pi, and that requires that x = 5 or -5.