A circle tangents to a hyperbola! (Harvard-MIT math tournament) @blackpenredpen

Uploaded April 2024 | Updated September 2026, 2 weeks ago

A circle is tangent to both branches of the hyperbola x^2-20y^2=24 (notice the "2024"?) as well as the x-axis. What is the area of the circle? You might think this is like a standard Calculus 1 problem and yes you would be right. However, the official solutions do not use calculus and I do not understand both.

This question is Q24 from the Guts round of the 2024 Harvard-MIT Math Tournament: hmmt-archive.s3.amazonaws.com/tournaments/2024/feb/guts/solutions.pdf

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A circle tangents to a hyperbola! (Harvard-MIT math tournament)

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