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

Question

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Thanks

anonymous · Answer

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

anonymous · Answer

There may be a better way of doing this..

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Medal now.