## Calculus (3rd Edition)

${\left( {x + y} \right)^2} = xy + 6$ as an equation in polar coordinates: ${r^2} = \frac{6}{{1 + \cos \theta \sin \theta }}$
Write ${\left( {x + y} \right)^2} = xy + 6$ ${x^2} + 2xy + {y^2} = xy + 6$ ${x^2} + {y^2} + xy = 6$ Since $x = r\cos \theta$ and $y = r\sin \theta$, we get ${x^2} + {y^2} = {r^2}$. So, ${r^2} + {r^2}\cos \theta \sin \theta = 6$ ${r^2} = \frac{6}{{1 + \cos \theta \sin \theta }}$