1988 AIME Problem 14

Past Contests AIME AIME - 1988
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1

Let C be the graph of x y=1, and denote by C^{*} the reflection of C in the line y=2 x. Let the equation of C^{*} be written in the form

12 x^{2}+b x y+c y^{2}+d=0 .

Find the product b c.