The vertex of the parabola is at the origin, its directrix passes through a focus F1 of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 1), and is perpendicular to the major axis of the ellipse The vertex of the parabola is at the origin, and its quasilinear passes through a focus F1 of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 1), and is perpendicular to the major axis of the ellipse. The intersection of the parabola and the ellipse is m (2 / 3, 2 radical 6 / 3). Solve the parabola and the elliptic equation

The vertex of the parabola is at the origin, its directrix passes through a focus F1 of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 1), and is perpendicular to the major axis of the ellipse The vertex of the parabola is at the origin, and its quasilinear passes through a focus F1 of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 1), and is perpendicular to the major axis of the ellipse. The intersection of the parabola and the ellipse is m (2 / 3, 2 radical 6 / 3). Solve the parabola and the elliptic equation

Let y2 = 2px (P > 0)
∵ point m (2 / 3,2 √ 6 / 3) is on the parabola, ∵ P = 2
y²=4x
∴F1（-1,0）,F2（1,0）,C=1
∴ 2a=MF1+MF2=4,a=2,b=√3
x²／4+y²／3