Math Help - differential geometry

1. differential geometry

Given $\{(u,v) \in R^2|u^2+v^2<1\}$ with $E=G=\frac{4}{(1-u^2-v^2)^2}$ and $F=0$. How do I show that an euclidean circle with center at the origin is a hyperbolic circle?

2. Calculate the Gauss curvature on such a circle.