## Thomas' Calculus 13th Edition

The conversion of polar coordinates and Cartesian coordinates are described as follows: 1. $r^2=x^2+y^2$ and $r=\sqrt {x^2+y^2}$ 2. $\tan \theta =\dfrac{y}{x} \implies \theta =\tan^{-1} (\dfrac{y}{x})$ 3. $x=r \cos \theta$ and 4. $y=r \sin \theta$ Given: $r^2 \sin^ 2 \theta=r \cos \theta$ Thus, the Cartesian equation is $y^2=x$ Hence, this shows a side-way parabola whose vertex at the origin open towards right.