Take this bezier curve

A = -5, 3 (starting point)

C1 = -1,11

C2 = 3, 19

B = 7, -37 (finishing point)

E divides AC1, F divides C1C2, G divides C2B, H divides EF, I divides FG, and P divides HI all in the ratio 1:3

After calulations, P is found to be -2, 8

Then the same coordinates divide the line segments in the ratio t:1-t

P then comes out to be 12t -5, -64t^3 + 24t + 3

Substituting t = 0 and t = 1 into P, it can be seen that P is at A and at B.

Now, my questions are these: (these involve P = 12t -5, -64t^3 + 24t + 3)

1. What values of t determine the points C1 and C2?

2. What is now the value of P if the coordinates divide their respective line segments in half?

Any help would be greatly appreciated

Thanks in advance