Polar Equation to Rectangular

Question

$$r=\frac{9}{4 \cos θ − 3 \sin θ}$$

How do I do this? (Equation is in polar form.)

I have already tried to do this, but I don't know how to finish it.

Answer 1

If you multiply on the right by $\frac rr$ the denominator will contain terms like $r \cos \theta$. Do you recognize that? Then just substitute $r=\sqrt {x^2+y^2}$

Answer 2

Multiply both sides of your equation by the denominator of the right hand side. This will remove all fractions.

If you then multiply out the new left hand side, you will get $r\cos\theta$ and $r\sin\theta$. You should know what those translate to in Cartesian coordinates in terms of $x$ and $y$. Do those replacements and you are done.