设A(x1,y1)B(x2,y2)M(x0,y0)
由于直线l倾斜角为a=45°
则：kl=tana=1
由于l过双曲线x^2/9-y^2/16=1的右焦点F(5,0)
则l:y-0=1*(x-5) (点斜式)
即：y=x-5,联立x^2/9-y^2/16=1
得：16x^2-9(x-5)^2=16*9
7x^2+90x-9*41=0
则：x1+x2=-90/7
则：y1+y2=(x1-5)+(x2-5)=x1+x2-10=-160/7
则：x0=(x1+x2)/2=-45/7,y0=(y1+y2)/2=-80/7
则：MF
=√[(x0-5)^2+(y0-0)^2]
=√[2*(80/7)^2]
=(80√2)/7