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- Feb 14, 2012

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I recently found an interesting problem which I initially thought I could solve without much trouble, but after I started to work on it, I found out that this has not been the case and this problem has driven me crazy, as I find no good way to attack it...so, I desperately need some help on this problem.

Problem:

The graph $xy=1$ is reflected in $y=2x$ to give the graph of $12x^2+rxy+sy^2+t=0$. Find $rs$.

I tried to sketch its graph and here is my sketch:

I managed only to get down to finding the relation between $r$ and $s$, i.e. $(3r+s=-33)$, but not the value of the product of them.

Thanks in advance for any help that anyone can offer.