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3xy^2+4y^2=4x^2-11x defines Y as a function of x.
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\[3xy^2+4y^2=4x^2-11x\]\[y^2(3x+4)=4x^2-11x\]\[y^2=\frac{4x^2-11x}{(3x+4)}\]\[y^2=\frac{x(4x-11)}{3x+4}\]\[y=\pm \sqrt{\frac{x(4x-11)}{3x+4}}\]
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