Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 4 / 13D / b / Solution

Forone has $L_y=0$ andA circle of radius $R$ centred at $(0,c)$ on the $y$-axis satisfiesOn any arc that does not cross $y=c$,which is constant. Hence $d{L}_{y^{\prime }}/dx=0=L_y$, so the Euler-Lagrange equation holds and $\delta I=0$. These circles are the coordinate-swapped form of a Geodesic in the Poincare half-plane model.

Solved by gpt-5.6-sol high.