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Hyperbola Reflection Line Equation Coefficients

2050SpecialistCoordinate GeometryTransformations

AIME · 1988 · Problem 14

Let $C$ be the graph of $xy = 1$, and denote by $C^*$ the reflection of $C$ in the line $y = 2x$. Let the equation of $C^*$ be written in the form $$12x^2 + bxy + cy^2 + d = 0.$$ Find the product $bc$.
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