How do I convert this parametric expression to an implicit one I have:
$$x=5+8 \cos \theta$$
$$y=4+8 \sin \theta$$
With $ -\frac {3\pi}4 \le \theta \le 0$
If I wanted to write that implicitly, how would I do it? I get that it's a circle, and I can easily write the circle implicitly, but I'm not sure how to convert the domain from $ -\frac {3\pi}4 \le \theta \le 0$ to a suitable domain in x and y.
I can think of a way to do it that would involve using the $Min$ function, but is that allowed in an implicit representation?

Just compute the range of $x,y$, or using the geometric meaning of polar coordinate, draw a picture to see how $x,y$ changes on the circle when $\theta$ changes.
The result is $x\in[5-4\sqrt{2},13],y\in[-4,4]$, where $x,y$ satisfies $(x-5)^2+(y-4)^4=8^2$.
