Posted by Sarah on Wednesday, March 13, 2013 at 8:22pm.
I'm extremely confused on what to do in part a of this question.
Consider the curve given by x=3sin(theta), y=1+2cos(theta), 0<=theta<=3pi/2
(a) Eliminate the parameter and find a Cartesian (Rectangular) equation for the curve.

Calculus  Reiny, Wednesday, March 13, 2013 at 8:36pm
Your basic replacement identities are:
r^2 = x^2 + y^2
x = rcosØ and y = rsinØ or cosØ = x/r and sinØ = y/r
so you have:
x =3sinØ > sinØ = x/3
y = 1+2cosØ
cosØ = (y1)/2
but we know sin^2 Ø + cos^2 Ø = 1
x^2/9 + (y1)^2 /4 = 1
looks like an ellipse to me