A municipal park has a circular jogging track whose centre is at C(2,−1) and whose radius is 5 m.
(i) Write the equation of the jogging track.
(ii) Three lamp posts are to be installed at L1(7,−1), L2(2,4) and L3(−1,−5). For each location, determine whether the lamp post will stand inside the track, on the boundary, or outside the track. Show all numerical work leading to your conclusion.