8. (3rd American Invitational Mathematics Examination) An ellipse in the $xy$-plane has foci at $(9,20)$ and $(49,55)$, and is tangent to the $x$-axis. Find the length of the major axis.
8. Make the point $F_{2}(49,55)$ symmetric to the $x$-axis to get $F^{\prime}{ }_{2}(49,-55)$. Suppose the ellipse is tangent to the $x$-axis at point $P$, then from $\angle F_{1} P O=$ $\angle F_{2} P x$, we know that $F_{1}, P, F_{2}^{\prime}$ are collinear, so the major axis $2 a=\left|F_{1} P\right|+\left|F_{2} P\right|=\left|F_{1} P\right|+\left|F^{\prime}{ }_{2} P\right|=\left|F_{1} F^{\prime}{ }_{2}\right|=$ $\sqrt{(49--9)^{2}+(-55-20)^{2}}=85$.