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There exits the option frame, which, in fact, you can directly use in show. Try:

var("x,y")
implicit_plot(x^2-y^2-1, (x,-2,2), (y,-2,2), frame=False, axes=True)

There exits exists the option frame, which, in fact, you can directly use in show. Try:

var("x,y")
implicit_plot(x^2-y^2-1, (x,-2,2), (y,-2,2), frame=False, axes=True)