If then . (You don't have to flip the thing upside down like that. It's just that I know the formula for but not the formula for .)

Write . Then . That is a quadratic equation for t, with solutions t=–3, t=1/3. Taking t=1/3, you get and , and you can plug those values into the formula for rotating axes. You could equally well take t=–3, which would have the effect of rotating the axes in the opposite direction. In either case, you should end up with an equation without an x'y' term.