An ellipse has foci at (9, 20) and (49, 55) in the xy plane and is tangent to x-axis. The length of major axis of ellipse is _____________

$S(9,20)S\text{'}(49,55)$

$b^2=\left(20\right)\left(55\right)=\left(4\right)\left(5\right)\left(5\right)\left(11\right)\Rightarrow b=\left(2\right)\left(5\right)\sqrt{11}=10\sqrt{11}$

$2ae=SS\text{'}=\sqrt{{40}^2+{35}^2}=5\sqrt{113}$

$ae=\frac{5}{2}\sqrt{113}$

$a^2=b^2+a^2{e}^2={\left(10\right)}^2\left(11\right)+\frac{25}{4}\left(113\right)=\frac{\left(25\right)\left(289\right)}{4}\Rightarrow a=\frac{\left(5\right)\left(17\right)}{2}\Rightarrow 2a=85$