1988 AIME 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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.