(1) The first step is to find the parabolic equation. Because the parabola passes through the (0,0) point, let the equation Y=ax? +bx, 4a+b = 0 is brought into the point (4,0); The solution of the two equations is b=-4a, and the original equation is: Y=ax? A= 1 of the (2, -4) solution of -4ax is brought into the characteristic point (the point is on a parabola), and the parabolic equation is: Y=x? -4x, from the perspective of parabola symmetry, OE=AE, while tantaoe = 4/2 = 2 ≠1(tant45 =1), BOE is not equal to 90, so □OEAB is a diamond.

(2)① Bring (2-2 equation 3, m) into the equation, m=4-8 equation 3+ 12-8+8 equation 3 = 8; At this time, OE≠AE (defined by angle bisector, the bisector of angle OEA is known to pass through point (2,0), so OE=AE, so □OEAB parallelogram.

(2) Suppose there is e (x, y), the first question knows that □OEAB is a diamond, the diagonals of the diamond are perpendicular to each other, and the focus of AO and BE is ks = ao * be = ao * 2ek = 4 * 2 * Y=12, and y = 3/2 of the solution; 3/2=x into the equation? -2x for 4x? For -8x-3=0, x1= (the root of 8 is 88)/4.

X 1=(8+ root number 88)/4; So it exists. E is ((8+ root number 88)/4,3/2) or ((8+ root number 88)/4,3/2).