Express this curve in the rectangular form 
Express the curve $r = \dfrac{9}{4+\sin \theta}$ in rectangular form. 
  And what is the rectangular form?

If I get the expression in rectangular form, how am I able to convert it back to polar coordinate?

$$
4r + 4r\sin\theta = 9.
$$
Therefore
$$
\sqrt{x^2+y^2} + 4y = 9.
$$
$$
\sqrt{x^2+y^2} = 9 - y.
$$
Now square both sides and go on from there.
But remember that squaring both sides can lead to extraneous roots.  For example $3^2=9$ and $(-3)^2=9$, so a "$\pm$" is introduced when you go back to the unsquared form.  In other words, the graph you get after squaring may contain additional points beyond those you should get, and you have to check for those.
