Now you should also know that
where is a constant (conservation of angular momentum).
I think you might need to know the angle that the initial velocity makes with before you can calculate the value of .
Substitute from equation (2):
Substitute , equation (2) and equation (3) into equation (1) and simplify to get the required DE (well, it's a DE for as a function of - good enough).
Now show that the solution to this DE is a circle (note: the solution is in polar form).