<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] $$r = \frac {6}{1-\sinθ}$$
$${r-r\sinθ}=6$$
$$\sqrt{x^2 + y^2}-y=6$$
$$\sqrt{x^2 + y^2}=y+6$$ now squaring both side and simplyfying we get
$$y = \frac{1}{12} x^2 -3$$
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