I approach these questions by assuming that the two equations are equal at the point where the graph shifts from one to the other. This follows from the fact that a continuous function must have for each f(x,y) a limit that equals this value as well from either side.

So set them equal,

The x's cancel which makes sense because the restriction is dependent on y, not x.

Now this equality isn't true for all (x,y), it is only at the point around y=1-c. So if you plug in 1-c for y and solve for c, you should get the desired value.