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

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) $y=r \sin \theta$ On multiplying with $r^2 \cos^2 \theta$ on both sides, we get $r^2 \cos^ 2 \theta=4r \sin \theta$ Therefore, our Cartesian equation is $x^2=4y \implies y=\dfrac{1}{4}x^2$ This shows a parabola whose vertex at the origin open upwards.