Show that the set S := {$\displaystyle (x,y) \in R^2 : x^2 + y^2 = 1$} is compact and connected.

To show it is compact, I would need to find a finite open cover for S... I think... but I really have no idea what that means

And for it being connected, that means S cannot be written as two disjoint open sets, but again, I don't know how to prove that, since our professor only just introduced the topic....

thanks for any help you can provide!