Here is an example of the way to use the implicit plot function in Maple.  

The text in red  is what you type, any text in blue is what the computer outputs.  When you use the "implicitplot" function, you must enter three parameters.  The first is the equation , the second is the values of x  that you want to consider, and the third is the values for y .  If the origin is a singular point for your curve, use the values I have used below to avoid the singular point (0,0) where the Implicit Function Theorem does not hold.  

Once you have plotted your curve in all four quadrents of the plane, you can glue it together on paper to see the curve.

>    with(plots);

[animate, animate3d, animatecurve, arrow, changecoords, complexplot, complexplot3d, conformal, conformal3d, contourplot, contourplot3d, coordplot, coordplot3d, cylinderplot, densityplot, display, displ...
[animate, animate3d, animatecurve, arrow, changecoords, complexplot, complexplot3d, conformal, conformal3d, contourplot, contourplot3d, coordplot, coordplot3d, cylinderplot, densityplot, display, displ...
[animate, animate3d, animatecurve, arrow, changecoords, complexplot, complexplot3d, conformal, conformal3d, contourplot, contourplot3d, coordplot, coordplot3d, cylinderplot, densityplot, display, displ...
[animate, animate3d, animatecurve, arrow, changecoords, complexplot, complexplot3d, conformal, conformal3d, contourplot, contourplot3d, coordplot, coordplot3d, cylinderplot, densityplot, display, displ...

>    implicitplot(x^2 = x^4 + y^4, x=0.001..1, y=0.001..1);

[Maple Plot]

>    implicitplot(x^2 = x^4 + y^4, x=0.001..1, y=-0.001..-1);

[Maple Plot]

>    implicitplot(x^2 = x^4 + y^4, x=-0.001..-1, y=0.001..1);

[Maple Plot]

>    implicitplot(x^2 = x^4 + y^4, x=-0.001..-1, y=-0.001..-1);

[Maple Plot]

>