Let a focus of the ellipse C: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) coincide with the focus of the parabola C: y ^ 2 = 8x, the eccentricity e = 2 radical 5 / 5, the right focus f passing through the ellipse be a straight line L not coincident with the coordinate axis, intersecting the ellipse at two points a and B. let m (1,0), and (MA vector + MB vector) ⊥ AB vector, find the equation of the straight line L

Let a focus of the ellipse C: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) coincide with the focus of the parabola C: y ^ 2 = 8x, the eccentricity e = 2 radical 5 / 5, the right focus f passing through the ellipse be a straight line L not coincident with the coordinate axis, intersecting the ellipse at two points a and B. let m (1,0), and (MA vector + MB vector) ⊥ AB vector, find the equation of the straight line L

(1) Let the right focus of the ellipse be (C, 0),
Because the focus coordinate of y2 = 8x is (2,0), so C = 2
Because e = C / a = 2 √ 5 / 5, then a ^ 2 = 5, B ^ 2 = 1
So the elliptic equation is: x ^ 2 / 5 + y2 = 1
(2) F (2,0) is obtained from (I),
Let the equation of l be y = K (X-2) (K ≠ 0)
Substituting x ^ 2 / 5 + y2 = 1, we get (5K ^ 2 + 1) x ^ 2-20k ^ 2x + 20K ^ 2-5 = 0,
Let a (x1, Y1), B (X2, Y2),
Then X1 + x2 = 20K ^ 25 / K ^ 2 + 1, x1x2 = 20K ^ 2 - √ 5 / 5K ^ 2 + 1,
∴y1+y2=k（x1+x2-4）,y1-y2=k（x1-x2）
∴ MA→+MB→=(x1-1,y1)+(x2-1,y2)=(x1+x2-2,y1+y2),AB→=(x2-x1,y2-y1)
∵ (MA→+MB→)•AB→=0,∴（x1+x2-2）（x2-x1）+（y2-y1）（y1+y2）=0∴ 20k^2×5^k2+1-2-4k2^×5k2+1=0,
∴ 3^k2-1=0,k=±√3/3
So the equation of line L is y = soil √ 3 / 3 (X-2)