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December 19, 2014

December 19, 2014

Posted by **Sarah** on Wednesday, March 13, 2013 at 8:22pm.

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 8:36pmYour basic replacement identities are:

r^2 = x^2 + y^2

x = rcosŲ and y = rsinŲ or cosŲ = x/r and sinŲ = y/r

so you have:

x =3sinŲ ---> sinŲ = x/3

y = 1+2cosŲ

cosŲ = (y-1)/2

but we know sin^2 Ų + cos^2 Ų = 1

x^2/9 + (y-1)^2 /4 = 1

looks like an ellipse to me

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