Question

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.
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 = (y-1)/2

but we know sin^2 Ø + cos^2 Ø = 1
x^2/9 + (y-1)^2 /4 = 1

looks like an ellipse to me

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