Making the usual substitutions (x=r·cos(θ), y=r·sin(θ)), you have
(r·cos(θ))² +4r·cos(θ) +4 + (r·sin(θ))² -4r·sin(θ) +4 = 8
r(r +4·cos(θ) -4·sin(θ)) = 0
Dividing by r then subtracting the non-r terms gives
r = 4(sin(θ) -cos(θ))
(r·cos(θ))² +4r·cos(θ) +4 + (r·sin(θ))² -4r·sin(θ) +4 = 8
r(r +4·cos(θ) -4·sin(θ)) = 0
Dividing by r then subtracting the non-r terms gives
r = 4(sin(θ) -cos(θ))