2022 AIME II Problem 12

Let a, b, x, and y be real numbers with a>4 and b>1 such that

\frac{x^{2}}{a^{2}}+\frac{y^{2}}{a^{2}-16}=\frac{(x-20)^{2}}{b^{2}-1}+\frac{(y-11)^{2}}{b^{2}}=1

Find the least possible value of a+b.