Given that the straight line and parabola y ＾ 2 = 2px intersect at two points AB, and OA ⊥ ob, OD ⊥ AB intersect at D, D coordinate is (2,1), find the value of P First, I calculate the slope k of OD with the coordinates of point D, and then calculate the slope k 'of ab. because AB passes through D, we can know the equation of ab Then, the equation AB is substituted into the parabola, and the x 1 + x 2 and X 1x 2 are calculated by the Weida theorem Then, let a (x1, root 2px1), B (X2, root 2px2), calculate the algebraic formula of OA, OB length, because OA ⊥ ob, so the area is oaob / 2 Then calculate the length of AB section parabola, OD length and area abod / 2 with chord length formula Finally, because the two areas are equal, abod / 2 = oaob / 2, and then combined with vedadine to understand P

Given that the straight line and parabola y ＾ 2 = 2px intersect at two points AB, and OA ⊥ ob, OD ⊥ AB intersect at D, D coordinate is (2,1), find the value of P First, I calculate the slope k of OD with the coordinates of point D, and then calculate the slope k 'of ab. because AB passes through D, we can know the equation of ab Then, the equation AB is substituted into the parabola, and the x 1 + x 2 and X 1x 2 are calculated by the Weida theorem Then, let a (x1, root 2px1), B (X2, root 2px2), calculate the algebraic formula of OA, OB length, because OA ⊥ ob, so the area is oaob / 2 Then calculate the length of AB section parabola, OD length and area abod / 2 with chord length formula Finally, because the two areas are equal, abod / 2 = oaob / 2, and then combined with vedadine to understand P

The landlord's method is very complicated, but we can recommend a better method: the slope of two vertical lines is - 1
That is to say, if we regard OA ob as two straight lines, because we know the slope of the straight line, we can set the unknown a B to represent OA ob two straight lines. According to the conclusion I gave, we can get the analytical formula of the instrument about AB, and then AB two points are on the parabola, we can get an analytical formula, and then we can get the result