10th British Mathematical Olympiad 1974 Problems

10th British Mathematical Olympiad 1974 Problems1.  C is the curve y = 4x2/3 for x ≥ 0 and C' is the curve y = 3x2/8 for x ≥ 0. Find curve C" which lies between them such that for each point P on C" the area bounded by C, C" and a horizontal line through P equals the area bounded by C", C and a vertical line through P.