a. Determine all points P(x, y) such that (0,0),(1,1),(1,0) and P are vertices of a parallelogram.
b. Two parallel lines intersect the (horizontal) parabola x=y^{2} at four distinct points: (0,0), (1,1),(9,3) and Q. Determine all possible coordinates of the point Q.
c. Two parallel lines intersect the parabola x=y^{2} at four distinct points: (0,0),(1,1),\left(a^{2}, a\right) and V. Here a \neq 0, \pm 1 is a real number. Determine all possible coordinates of the point V. The answer should be expresed in term of a.