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the first issue is probably because you didn't define the variable y, this can be done typing y = var('y'). The fact that this is not necessary for the x variable is because it is predefined at the startup of Sage. If you find yourself using very often the variable y (or other variables or functions), then it's possible to load them at startup by using the init.sage file, as explained in sage startup scripts.

for the questions on plotting, you may consider these functions as starting point:

• implicit_plot, see implicit plots doc
• parametric_plot for parametric plots in 2d and parametric_plot3d, see parametric plots 3d doc