Question 161: In the Cartesian coordinate system, there is an ellipse with its two foci at $(9,20)$ and $(49,55)$, and the ellipse is tangent to the $x$-axis. Then the length of the major axis of the ellipse is $\qquad$.


Question 161, Answer: Let $F_{1}(9,20), F_{2}(49,55)$. Suppose $E$ is the point symmetric to $F_{2}$ with respect to the $x$-axis, then $E(49,-55)$. According to the optical property of an ellipse, the length of the major axis of the ellipse is $\left|\mathrm{F}_{1} \mathrm{E}\right|=$
$$
\sqrt{(9-49)^{2}+(20-(-55))^{2}}=85
$$