Answer
A parabola whose vertex at the origin open upwards.
Work Step by Step
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. $y=r \sin \theta$
Multiply both sides the given equation by $r^2 \cos^2 \theta$
Now, we have $r^2 \cos^ 2 \theta=4r \sin \theta$
Thus, the Cartesian equation is $x^2=4y$
or, $y=\dfrac{1}{4}x^2$
Hence, this shows a parabola whose vertex at the origin open upwards.
