The letters x and y represent the rectangular coordinates. Write each equation using polar corrdinates (r, theta).
(1) 4x^(2) y = 1
(2) y = -3
I'll try (2):
When converting from rectangular coordinates to polar keep these three things in mind.
1. $\displaystyle x=r \cos \theta$
2. $\displaystyle y=r \sin \theta$
3. $\displaystyle r^2 = x^2+y^2$
$\displaystyle y=r \sin \theta$
Substituting,
$\displaystyle r \sin \theta = -3$
$\displaystyle r=-\frac{3}{\sin \theta}=-3 \csc \theta$
Okay, here's (1):
$\displaystyle 4(r\cos\theta)^2 \cdot r\sin\theta=1$
$\displaystyle 4r^2\cos^2\theta \cdot r \sin\theta=1$
$\displaystyle 4r^3\cos^2\theta \sin\theta=1$
$\displaystyle r^3=\frac{1}{4\cos^2 \theta \sin \theta}$
$\displaystyle r=\sqrt[3]{\frac{1}{4\cos^2 \theta \sin \theta}}$