So c = 5 and b =-6.

So the parabola is y = x 2-6x+5.

The straight line BC is x+y=5.

2. The two intersections of parabola and X axis are (1, 0) and (5, 0) respectively.

Let m (t, t 2-6t+5), 1

Therefore, Mn = 5-t-(t 2-6t+5) =-t 2+5t, 1

Therefore, when t=5/2, MN is the largest, and the maximum value is 75/4.