
1) with Cartesian equation, thanks to Piers Barber: a^{4} y^{4}  4 a^{3} c x y^{3} + 2 a^{2} c y^{3} + 6 a^{2} c^{2} x^{2} y^{2}  4 a c^{2} x y^{2}  2 a^{3} x y^{2}  2 a^{2} c^{2} y^{2} + c^{2} y^{2} + a^{2} y^{2}  4 a c^{3} x^{3} y + 2 c^{3} x^{2} y + 4 a^{2} c x^{2} y + 4 a c^{3} x y 2 c^{3} y  4 a^{2} c y + c^{4} x^{4}  2 a c^{2} x^{3}  2 c^{4} x^{2} + c^{2} x^{2} + a^{2} x^{2} + 2 a c^{2} x = a^{2} + c^{2}  c^{4}
