As shown in the figure, the parabola is symmetric about X axis, its vertex is at the origin of coordinates, and the points P (1,2), a (x1, Y1), B (X2, Y2) are all on the parabola. (I) write out the equation of the parabola and its quasilinear equation; (II) when the slopes of PA and Pb exist and complement each other, find the value of Y1 + Y2 and the slope of line ab

As shown in the figure, the parabola is symmetric about X axis, its vertex is at the origin of coordinates, and the points P (1,2), a (x1, Y1), B (X2, Y2) are all on the parabola. (I) write out the equation of the parabola and its quasilinear equation; (II) when the slopes of PA and Pb exist and complement each other, find the value of Y1 + Y2 and the slope of line ab

(1) Let the equation of parabola be y2 = 2px ∵ point P (1,2) on the parabola be 22 = 2p × 1, then p = 2. So the equation of parabola is y2 = 4x, and the equation of Quasilinear is x = - 1 (II). Let the slope of straight line PA be kPa, and the slope of straight line Pb be KPB, then kPa = Y1 − 2x1 − 1 (x1 ≠ 1), KPB = Y2 − 2