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 \(bc\).

(第六届AIME1988 第14题)