Parameterizing an ellipse

Question

Given the ellipse $(x-1)^2 + \frac{y^2}{4}= 1$, parametrize the curve in polar coordinates.

I've forgotten something very basic here. Can someone help get me started?

Answer 1

HINT:

$$(x-1)^2 + \frac{y^2}{4}= 1$$

$$(x-1)^2 + (\frac{y}{2})^2= 1 \tag 1$$

$$x=r\cos \theta \tag 2$$

$$y=r\sin \theta \tag 3$$

Put in Equation 1

$$(x-1)^2 + (\frac{y}{2})^2= 1$$

$$(r\cos \theta-1)^2 + (\frac{r\sin \theta}{2})^2= 1$$

Find r as function of $\theta$