#### Answer

$$3x^2 -2x +4y^2=1.$$

#### Work Step by Step

We have $$r=\frac{1}{2-\cos\theta}\Longrightarrow 2r-r\cos\theta =1.$$
Recall that $r\cos \theta=x$ and $r^2=x^2+y^2$:
Hence, we get
$$ 2\sqrt{x^2+y^2}-x =1\Longrightarrow 4(x^2+y^2)=(1+x)^2=1+2x+x^2.$$
Finally, we get
$$3x^2 -2x +4y^2=1.$$