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)