How do I derive parametric functions for drawing a curve given by an equation?

Question

If I have an equation in two unknowns, such as $$2x^4 + yx^2 + y^4 = 2$$ how do I derive the two corresponding parametric functions $x(y)$ and $y(t)$ that I could use for drawing the curve that the equation represents? The simple approach I seem to find everywhere of setting $x(t) = t$ and simply isolating $y(t)$ correspondingly from the equation does not seem to work for me here due to the $xy^2$ product term.