Hyperbola problem: F1 and F2 are the left and right focus of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0), Given that F1 and F2 are the left and right focus of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0), if there is a point a on the right branch, so that the distance between point F2 and straight line AF1 is 2a, then the value range of eccentricity of the hyperbola is Given that F1 and F2 are the left and right focus of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0), if there is a point a on the right branch, so that the distance between point F2 and straight line AF1 is 2a, what is the range of eccentricity of the hyperbola

Hyperbola problem: F1 and F2 are the left and right focus of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0), Given that F1 and F2 are the left and right focus of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0), if there is a point a on the right branch, so that the distance between point F2 and straight line AF1 is 2a, then the value range of eccentricity of the hyperbola is Given that F1 and F2 are the left and right focus of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0), if there is a point a on the right branch, so that the distance between point F2 and straight line AF1 is 2a, what is the range of eccentricity of the hyperbola

Let a point coordinate (m, n) be (m, n), then the left focus F1 (C, 0) and a point are (M + C) y-n (x + C) = 0, and the distance from the right focus F2 (C, 0) to the straight line n (c + C) 124; / 124| / \124\ (c + C) 124\\\\\ (c) (n (C, 0) F1 (C (C, 0) and the left focus F1 (C, 0) F1 (C (C, 0) and a point, then the left focus F1 (C, 0) and a point is (M + C) y (M + C) y (M + C) y (c) y-y-y-y-y-y-n) y-n (x-y-y-y-y-n) y-n (x-n) and/ n) &;;
Because a is a point on hyperbola, so (M & # 178 / / A & # 178;) - (n & # 178 / / B & # 178;) = 1, → (M / N) = (A & # 178 / / B & # 178;) + (A & # 178 / / N & # 178;);
So E & # 178; = 1 + (A & # 178; / B & # 178;) + (A & # 178; / N & # 178;) > 1 + (A & # 178; / B & # 178;) = 1 + [A & # 178; / (C & # 178; - A & # 178;)] = 1 + [1 / (E & # 178; - 1)] → E & # 178; - 1 > 1 / (E & # 178; - 1) → E & # 178; - 1 > 1;
That is, E > 2;