Answer
This equation describes a hyperbola with foci on the x-axis, centered at $(0,0)$.
Work Step by Step
$r^2cos(2\theta) = 1$
** Remember: $cos (2x) = cos^2x - sin^2x$
$r^2 (cos^2(\theta) - sin^2(\theta)) = 1$
$r^2 cos^2(\theta) - r^2sin^2(\theta) = 1$
** Notice: $rcos(\theta) = x$ and $rsin(\theta) = y$
$x^2 - y^2 = 1$
As we can see in the Cartesian equation, this curve is a hyperbola with foci on the x-axis, centered at $(0,0)$.
