Answer
A parabola whose vertex at the origin open upwards.
Work Step by Step
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.
