It is known that the eccentricity of ellipse C: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) e = √ 2 / 2, the left and right focal points are F1, F2 and P (2, √ 3) Let the line L: y = KX + m intersect with the ellipse C at two points M. n. the inclination angles of the lines F2m and f2n are α, β, and α + β = π (PIE). Let's ask whether the line L passes the fixed point? If so, find the coordinates of the point

It is known that the eccentricity of ellipse C: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) e = √ 2 / 2, the left and right focal points are F1, F2 and P (2, √ 3) Let the line L: y = KX + m intersect with the ellipse C at two points M. n. the inclination angles of the lines F2m and f2n are α, β, and α + β = π (PIE). Let's ask whether the line L passes the fixed point? If so, find the coordinates of the point

Mn has a slope, let y = KX + M
x²／2+y²=1.y=kx+m
（2k²+1）x²+4kmx+2m²-2=0．
Let m (x1, Y1), n (X2, Y2),
X1 + x2 = - 4km / 2K & # 178; + 1, x1x2 = 2m & # 178; - 2 / 2K & # 178; + 1, kf2m = kx1 + m / x1-1, kf2n = kx2 + m / x2-1
From the known α + β = π,
kF2M+kF2N=0,
kx1+m／x1-1+kx2+m／x2-1=0．
2kx1x2+（m-k）（x1+x2-2m=0
∴ 2k•﹙2m²-2／2k²+1﹚-4km(m-k)／﹙2k²+1﹚-2m=0
m=-2k．
∴y=k（x-2）,（2,0）