Given the ellipse G: x ^ 2 + y ^ 2 / 4 = 1, make the tangent l of circle x2 + y2 = 1 through point P (0, m), and l intersect the ellipse g at two points a and B to find the focus coordinates and eccentricity of the ellipse G Try to express the absolute value of AB as a function of M, and find the maximum absolute value of ab

Given the ellipse G: x ^ 2 + y ^ 2 / 4 = 1, make the tangent l of circle x2 + y2 = 1 through point P (0, m), and l intersect the ellipse g at two points a and B to find the focus coordinates and eccentricity of the ellipse G Try to express the absolute value of AB as a function of M, and find the maximum absolute value of ab

A ^ 2 = 4, B ^ 2 = 1, C ^ 2 = 3. So the focus coordinates are (0, √ 3), (0, √ 3), and the eccentricity e = √ 3 / 2. Let the straight line be y = KX + m, because the straight line is tangent to the circle, so | m | / √ (K & # 178; + 1) = 1, so K & # 178; = M & # 178; - 1. The straight line and the ellipse are connected to obtain (4 + K & # 178;) x & # 178; + 2kmx + M & # 178; - 4 = 0 △ = 4K &