P is the point on the right branch of hyperbola x29-y216 = 1, m and N are the points on the circle (x + 5) 2 + y2 = 4 and (X-5) 2 + y2 = 1 respectively, then the maximum value of | PM | - | PN | is () A. 6B. 7C. 8D. 9

P is the point on the right branch of hyperbola x29-y216 = 1, m and N are the points on the circle (x + 5) 2 + y2 = 4 and (X-5) 2 + y2 = 1 respectively, then the maximum value of | PM | - | PN | is () A. 6B. 7C. 8D. 9

In the hyperbola x29-y2216 = 1, as shown in the figure: a = 3, B = 4, C = 5, \\\124; a = 3, as shown in the figure: \\\\\\\\\\124; a = 3, B = 4, C = 5, {F1 (- 5, 0), F2 (5,0), F2 (5,0), F2 (5,0), \\\\\\124; Pf1 || Pf1 |||| PF2 ||||||||124||||if ≤| Pf1 | + | MF1 | - | PF2 | + | NF2 | = 6 + 1 + 2 = 9