Let m be a positive integer. A tangent line at the point P on the parabola C1:y=x2+m2 intersects with the parabola C2:y=x2 at the points A, B. For the point Q between A and B on C2, denote by S the sum of the areas of the region bounded by the line AQ,C2 and the region bounded by the line QB, C2. When Q move between A and B on C2, prove that the minimum value of S doesn't depend on how we would take P, then find the value in terms of m. calculusintegrationconicsparabolageometrycalculus computations