Question

How do you convert the polar equation `r=2/(2-costheta)` into rectangular form?

Answer 1

`2sqrt(x^2+y^2)=2+x`

Explanation:

Use the conversion formula `r(cos theta, sin theta)=(x, y)` that gives

`cos theta=x/r and r=sqrt(x^2+y^2)`.

The answer follows.

The given equation has the form

`1/r=1-1/2 cos theta`, that represents an ellipse with

eccentricity `e =1/2` and semi major axis `a = 4/3`.

Graph is inserted

graph{2sqrt(x^2+y^2)-x-2=0 [-2.5, 2.5, -1.25, 1.25]}