Find a polar equation for the curve represented by the given Cartesian equation. $$x ^ { 2 } = 3 y$$
A) $r = 3 \tan \theta \sec \theta$
B) $r = 3 \sin \theta$
C) $r = 3 \tan \theta$
D) $r = 3 \cos \theta \sin \theta$
E) $r = 3 \tan \theta \csc \theta$

Question

Quizplus · Accepted Answer

To convert the Cartesian equation $x^2 = 3y$ to a polar equation, we use the relationships $x = r \cos \theta$ and $y = r \sin \theta$. Substituting these into the given equation, we get $(r \cos \theta)^2 = 3(r \sin \theta)$, which simplifies to $r^2 \cos^2 \theta = 3r \sin \theta$. Dividing both sides by $\cos^2 \theta$ and $r$, assuming $r \neq 0$, we get $r = 3 \tan \theta \sec \theta$.

Find a Polar Equation for the Curve Represented by the Given