It is known that a parabola is symmetric about x-axis, its vertex is the origin of coordinates, and points P (2,4), a (x1, Y1), B (X2, Y2) are three points of the parabola. (I) find the parabola (1) Find the equation of the parabola (2) If the inclination angles of PA and Pb are complementary, the trajectory equation of the midpoint of AB is obtained (3) If ab ⊥ PA, find the planting range of the ordinate of point B

It is known that a parabola is symmetric about x-axis, its vertex is the origin of coordinates, and points P (2,4), a (x1, Y1), B (X2, Y2) are three points of the parabola. (I) find the parabola (1) Find the equation of the parabola (2) If the inclination angles of PA and Pb are complementary, the trajectory equation of the midpoint of AB is obtained (3) If ab ⊥ PA, find the planting range of the ordinate of point B

Let f (x) = ax ^ 2 + BX + C; (I): the vertex is the origin of the coordinate, that is, f (0) = C = 0; and the axis of symmetry x = - B / (2a) = 0; and the parabola a cannot be zero, so B = 0; substituting point P (2,4) into the function, f (2) = a × 2 ^ 2 = 4, a = 1; to sum up, the equation of the parabola: F (x) = x ^ 2; (II): the inclination angle of the straight line PA and Pb complement each other