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Ellipses shared point minimum a plus b

2175ExpertCoordinate GeometryAlgebra

AIME II

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 for $a + b$.
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