[size=85] This applet illustrates an example of finding equations of branches of a plane curve of degree four (specified implicitly) using existing[b][url=https://www.geogebra.org/m/v4fvf8nx] rigorous solutions[/url][/b] in the form of complex functions in symbolic form.[br] The [b] [url=https://en.wikipedia.org/wiki/Quartic_plane_curve]Quartic plane curve[/url] [/b]of the [b]fourth order [/b]has 15 coefficients: A [b]x[/b][sup][b]4[/b][/sup]+B [b]y[sup]4[/sup][/b]+C [b]x[sup]3 [/sup]y[/b]+D [b]x[sup]2 [/sup]y[sup]2[/sup][/b]+E [b]x y[sup]3[/sup][/b]+F [b]x[sup]3[/sup][/b]+G [b]y[sup]3[/sup][/b]+H [b]x[sup]2 [/sup]y[/b]+I [b]x y[sup]2[/sup][/b]+J [b]x[sup]2[/sup][/b]+K [b]y[sup]2[/sup][/b]+L[b] x y[/b]+M[b] x[/b]+N [b]y[/b]+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.[br] Images of three examples are presented in the [url=https://www.geogebra.org/m/wmwsrksg]applet[/url][b].[/b][br][/size]