Solve
using the quadratic formula. You get solutions of the form y = mx where m is a function of c. There is only a certain set of values of c for which these lines exist. No level curves exist for values of c lying outside of these values.
Note: c = 0 gives the level curves x = 0 and y = 0 (which obviously pass through the origin).
Clearly this example is one of an infinite number of possibilities. I can only hope the OP has not been discouraged from contemplating it as a solution to his/her problem.