As shown in the figure, in the plane rectangular coordinate system xoy, the analytical expression of the parabola is
solution
(1) Let the analytic formula of parabola be y = a (x-1) (X-5), and substituting a (0,4) into it, the solution is a = 4 / 5. The analytic formula of parabola is
Y = 4 (x-1) (X-5) / 5 = 4 (x-3) ^ 2 / 5-16 / 5, x = 3
(2) The coordinates of point P (6,4)
(3) Let n [x, 4 (x-4 (x-4 (x-4 (x-4 (x-4 (x-3) (x-3 (x-3) (x-3) ^ 2 / 5-5-16 / 5], then E (x, - 4x / 5 + 4) is e (x, - 4x / 5 + 4), so en = - 4X / 5 + 4 - [4 (x-3) ^ 4 (4 (x-3) ^ 4 (x-4 (x-3) ^ 2 / 4 (4 (x-3) (4 (x-3) (4 (x-3) (4 (x-3) ^ 4 (4 (4 (x-3) ^ 4 (4 (4 (x-3) ^ 4 (4 (4 (x-3) ^ 4 (4 (4 (x-3) (4 (x-3) (4 (x-3) (4 (x-3) ^ 2 (x-3) ^ 2 / 2 / 2 / 2 / 3) ^ 2 / 2 / 2 / 5) / 2 / 5) / 2 / 5 when the coordinates are (5 / 2, - 3), the maximum area of △ NAC is 25 / 2
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