Question

Find a Cartesian equation for the curve and identify it. r^2cos2θ = 1

Answer 1

\[x=r \cos \theta ,y=r \sin \theta ,x ^{2}+y ^{2}=r ^{2},\tan \theta=\frac{ y }{x }\]
\[\cos 2\theta=\frac{ 1-\tan ^{2}\theta }{ 1+\tan ^{2}\theta } \]
substitute the values and simplify