It is known that the straight line and parabola y & # 178; = 2px (P > 0) intersect at two points a and B, and OA ⊥ ob, OD ⊥ AB intersect at point D, and the coordinates of point D are (2,1), Let's find the value of P instead of a vector,

Let a (x1, Y1) B (X2, Y2)
Because od slope is 1 / 2, OD ⊥ ab
The slope of AB is - 2,
So the linear AB equation is 2x + Y-5 = 0 ①
Substituting ① into the parabolic equation, we get
y^2+py-5p=0
Then y1y2 = - 5p
Because (Y1) ^ 2 = 2px1; (Y2) 2 ^ = 2px2
Then (y1y2) ^ 2 = 4 (P ^ 2) x1x2
So x1x2 = 25 / 4
Because OA ⊥ ob
Then x1x2 + y1y2 = 0
p=5/4

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