Finding explicit expressions of four real functions for an implicitly defined plane curve whose equation is biquadratic in the variable y
x⁴ + 2x² y² + a y⁴ - x³ + 3x y² = 0
Biquadratic equation, the solution y=y(x) of which is found by the formulas EqWorld. The branches of the implicit function generally correspond to the real functions f(x) on the considered domains of definition of the implicit function.
The vertical asymptotes are found using the implicit function theorem and the calculations are done in CAS.