As shown in the figure, in the plane rectangular coordinate system, the parabola y = - 1 / 2x & # 178; + 3 / 2x + 2 intersects X axis at two points a and B, and intersects Y axis at point C (1) ABC is a right triangle (2) : the straight line x = m (0 ∠ m ∠ 4) moves on the line ob, intersects the x-axis at point D, intersects the parabola at point E, intersects BC at point F. when m = what, EF = DF? (3) : after connecting CE and be, "is there a point e to maximize the area of triangle BCE?" if there is a point E, calculate the coordinates of point E and the maximum area of triangle BCE

As shown in the figure, in the plane rectangular coordinate system, the parabola y = - 1 / 2x & # 178; + 3 / 2x + 2 intersects X axis at two points a and B, and intersects Y axis at point C (1) ABC is a right triangle (2) : the straight line x = m (0 ∠ m ∠ 4) moves on the line ob, intersects the x-axis at point D, intersects the parabola at point E, intersects BC at point F. when m = what, EF = DF? (3) : after connecting CE and be, "is there a point e to maximize the area of triangle BCE?" if there is a point E, calculate the coordinates of point E and the maximum area of triangle BCE

(1) According to the meaning of the problem, the coordinates of a, B and C are (- 1,0), (4,0), (0,2), so AC ^ 2 = OA ^ 2 + OC ^ 2 = 1 + 4 = 5, BC ^ 2 = ob ^ 2 + OC ^ 2 = 16 + 4 = 20, AB ^ 2 = 25, so AC ^ 2 + BC ^ 2 = AB ^ 2, so the triangle ABC is a right triangle; (2) the analytic formula of BC is y = - X / 2 + 2, let