Points a and B are two moving points beyond the origin of the parabola y ^ 2 = 2px (P > 0), and OA is perpendicular to ob, Let a (x1, Y1), B (X2, Y2) find the values of Y1 * Y2 and X1 * x2

Points a and B are two moving points beyond the origin of the parabola y ^ 2 = 2px (P > 0), and OA is perpendicular to ob, Let a (x1, Y1), B (X2, Y2) find the values of Y1 * Y2 and X1 * x2

Substituting a (x1, Y1) into y ^ 2 = 2px (P > 0), we get X1 = Y1 ^ 2 / (2P)
Similarly, X2 = Y2 ^ 2 / (2P)
Multiply the two formulas to get X1 * x2 = (Y1 * Y2) ^ 2 / (4 * P ^ 2)
Let OA slope K1 and ob slope K2
k1=y1/x1,k2=y2/x2
Because OA is perpendicular to ob, K1 * K2 = - 1
Substituting into the above formula, K1 * K2 = (Y1 / x1) * (Y2 / x2) = - 1
After finishing, we get X1 * x2 = - Y1 * Y2
Substituting X1 * x2 = - Y1 * Y2 into X1 * x2 = (Y1 * Y2) ^ 2 / (4 * P ^ 2)
(y1*y2)^2/(4*p^2)=-y1*y2
Simplification
y1*y2*(y1*y2+4*p^2)=0
Because a and B are not at the origin, x1, Y1, X2 and Y2 are not zero,
So Y1 * Y2 + 4 * P ^ 2 = 0
y1*y2=-4*p^2,x1*x2=4*p^2