Question

How to convert x=3+3cos(theta) and y=2+5sin(theta) to rectangular by eliminating the parameter

Answer 1

\[
\frac{x-1}3=\cos(\theta)
\]

Answer 2

\[
\sin(\theta) =\pm\sqrt{1-\cos^2(\theta)} = \pm \sqrt{1-\left(\frac{x-1}3\right)^2}
\]

Answer 3

\[
y=2\pm 5\sqrt{1-\left(\frac{x-1}3\right)^2}
\]

Answer 4

Thanks

Answer 5

This parametrization can only be regularized for certain intervals of \(\theta\), otherwise it stops being a function.

Answer 6

There may be a better way of doing this..

Answer 7

\[
\frac{x-1}{3}=\cos(\theta)\\
\frac{y-2}{5} = \sin(\theta)\\
\left(\frac{x-1}{3}\right)^2+\left(\frac{y-2}{5}\right)^2 = \cos^2(\theta)+\sin^2(\theta) = 1
\]

Answer 8

So a less pelletty answer is just\[
\left(\frac{x-1}{3}\right)^2+\left(\frac{y-2}{5}\right)^2 = 1
\]

Answer 9

Medal now.