## University Calculus: Early Transcendentals (3rd Edition)

A hyperbola whose center is at the origin (0,0) with transverse axis $y=x$ and conjugate axis $y=-x$.
Conversion of polar coordinates and Cartesian coordinates are as follows: a)$r^2=x^2+y^2 \implies r=\sqrt {x^2+y^2}$ b) $\tan \theta =\dfrac{y}{x} \implies \theta =\tan^{-1} (\dfrac{y}{x})$ c) $x=r \cos \theta$ d) $y=r \sin \theta$ Here, $r^2 \sin 2 \theta=2$ can be written as $r^2 (2 \sin \theta \cos \theta)=2$ Thereforeg, our Cartesian equation is $xy=1 \implies y=\dfrac{1}{x}$ This shows a hyperbola whose center is at the origin (0,0) with transverse axis $y=x$ and conjugate axis $y=-x$.