LogFAQs > #889253626

I've puzzled over this for half an hour now, but I'm sure the answer is easy. I can't ask the tutoring center for help because I'm somewhere else today and they're closed on weekends. The question is simple: find a Cartesian equation for the curve (r^2)cos(2theta)=1.

I know r^2=x^2+y^2, and I know to use a double angle identity on cos(2theta). My problem is that the double angle identities (1-sin(theta)) and (2cos^2(theta)-1) lead me to x^2=1 and y^2=-1, both of which are obviously not the answer I need. This happens because I end up with something like r^2(1-sin^2(theta)=1, which just gets me r^2-r^2sin^2(theta)=1, and the r^2sin^2(theta) becomes a -y^2, which cancels out the other y^2 and leaves me just an x^2, which isn't helpful.

I know the answer will look something like x^2/something + y^2/something = something, but I have no idea how to keep the x^2 and y^2 from disappearing while removing the theta.
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Started: July 6, 2005