An example of finding explicit equations for curves using exact roots as complex functions that make up an implicitly defined quartic plane curve whose equation has 15 coefficients
This applet illustrates an example of finding equations of branches of a plane curve of degree four (specified implicitly) using existing rigorous solutions in the form of complex functions in symbolic form.
The Quartic plane curve of the fourth order has 15 coefficients: A x4+B y4+C x3 y+D x2 y2+E x y3+F x3+G y3+H x2 y+I x y2+J x2+K y2+L x y+M x+N y+P=0, where at least one of A, B, C, D and E is non-zero. You can explore these curves by adjusting the coefficients using the sliders.
Images of three examples are presented in the applet.