Ellipses with shared point minimum a+b

2175ExpertCoordinate GeometryAlgebra

AIME II · 2022 · 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 $a+b.$

0 students attempted0% solvedRating 2175

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Ellipses with shared point minimum a+b

2175ExpertCoordinate GeometryAlgebra

AIME II · 2022 · 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 $a+b.$

0 students attempted0% solvedRating 2175