In coordinate space, there is a point $\mathrm { A } ( 9,0,5 )$, and on the $xy$-plane there is an ellipse $\frac { x ^ { 2 } } { 9 } + y ^ { 2 } = 1$. For a point P on the ellipse, find the maximum value of $\overline { \mathrm { AP } }$. [3 points]