P is the point on the hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0), F1 and F2 are its focus, the eccentricity of the hyperbola is 5 / 4, and the vector pf * vector PF2 = 0, If the area of triangle f1pf2 is 9, find the value of a + B

P is the point on the hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0), F1 and F2 are its focus, the eccentricity of the hyperbola is 5 / 4, and the vector pf * vector PF2 = 0, If the area of triangle f1pf2 is 9, find the value of a + B

P is the hyperbola x ^ 2 / A ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0) point on the hyperbola x ^ 2 / A ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0, b > 0) point on the hyperbola x ^ 2 / A ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0, b > 0) point on the right branch, according to the definition of hyperbola, according to the definition of hyperbola, according to the definition of hyperbola, the right branch, according to the definition of hyperbola, according to the definition of hyperbola, we can define Pf1 Pf1 | PF2 | PF2 |||||||||\pf2 =