<s>[INST] Convert the equation to rectangular form $r = \frac {6}{1-\sinθ}$ Convert the equation to rectangular form $r = \frac {6}{1-\sinθ}$
The answer should be: $y = \frac{1}{12} x^2 -3$
But how to arrive at the answer?
I tried replacing r with $\sqrt{x^2 + y^2}$, then $\sinθ$ as $\frac{y}{r}$ but to no avail.
I also ended up with 
$r = \frac{6}{\frac{r-y}{r}} $ ->
$ 1 = \frac{6}{\sqrt{x^2+y^2}-y}$ -> x = +- 6
but that's not the answer...
 [/INST] Just multiply by denominator:
$$
r = \frac{6}{1-\sin\theta} \Longrightarrow r(1 - \sin\theta) = 6\Longrightarrow
r - y = 6
$$
Now
$$
\sqrt{x^2+y^2} = 6+y\Longrightarrow x^2 + y^2 = (6+y)^2,
$$
or
$$
x^2 = 36 + 12y \Longrightarrow y = \frac{x^2}{12} - 3
$$
</s>