AIME 2022b 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 $a+b.$