So the coordinate of point Q is (a+2,0).
The abscissa of point p' is a, and the ordinate = a 2 is obtained by substituting it into parabolic equation.
So p' (a, a 2)
Q' (A+2，(A+2) 2)
The slope of the straight line op' = a 2/a = a
The analytical formula of the straight line OP' is y-a 2 = a (x-a), that is, y=ax.
(2) The intersection point m between the straight line OP' and the vertical line y=a+2 of the X axis is (a+2, a(a+2)).
So the area of the trapezoid P' pqm =[ upper bottom+lower bottom] * height /2 = [a 2+a (a+2)] * 2/2 = 2a 2+2a.
The area of trapezoid P'PQQ' = [a 2+(a+2) 2] 2/2 = 2a 2+4a+4.
The straight line OP' bisects the area of the trapezoid P'pqq',
So the area of trapezoid P'PQM is half that of trapezoid P'PQQ.
So 2a 2+2a = 1/2 (2a 2+4a+4).
The solution is a= plus or minus root number 2.