The hyperbolic plane is a classic two-dimensional surface and can be used to describe spaces of constant negative curvature. It's defined by the metric

dl^2 = -y^2(dx^2+dy^2) for y greater than or equal to 0.

a) Show that points on the x-axis are an infinite distance from any point (x,y) in the upper half plane?
b) Write out the geodesic equations?