text: find a polar equation of the ellipse with focus at the pole...? (x+1)^2 /4 + y^2 /3 =1 wikipedia gives this in polar coordinates, where the origin is one focus of the ellipse:  r=a(1-e^2)/(1+ecos(theta))  by inspection your semimajor axis is 2 = a your semiminor is 3^0.5 so you have an eccentricity of 1/2   hopefully , if i haven't got it completely wrong,  r=3/2/(1+cos(theta)/2) should be what you want.