A point P with positive coordinates is common to all three curves given below:
1. y=x2
2. y2=4ax (where a is a positive constant)
3. 2y=3x+1
a. (i) Determine the coordinates of P by solving the three equations simultaneously.
b. (ii) Hence, find the value of the parameter a.
c. (iii) Investigate algebraically whether any real point other than P can satisfy all three equations at the same time.