# How do you find cartesian equation the parametric equations of a circle are x=cos theta -4 and y=sin theta + 1?

Oct 30, 2017

${\left(x + 4\right)}^{2} + {\left(y - 1\right)}^{2} = 1$

#### Explanation:

From $x = \cos \left(\theta\right) - 4$, $\cos \left(\theta\right) = x + 4$ and from $y = \sin \left(\theta\right) + 1$, $\sin \left(\theta\right) = y - 1$

Hence,

${\left(x + 4\right)}^{2} + {\left(y - 1\right)}^{2} = {\left(\cos \left(\theta\right)\right)}^{2} + {\left(\sin \left(\theta\right)\right)}^{2}$ or,

${\left(x + 4\right)}^{2} + {\left(y - 1\right)}^{2} = 1$