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Tangents to graphs of implicit relations

AP.CALC: FUN‑4 (EU), FUN‑4.D (LO), FUN‑4.D.1 (EK), FUN‑4.E (LO), FUN‑4.E.1 (EK), FUN‑4.E.2 (EK)


Consider the curve given by the equation x, y, squared, minus, x, cubed, y, equals, 8. It can be shown that start fraction, d, y, divided by, d, x, end fraction, equals, start fraction, 3, x, squared, y, minus, y, squared, divided by, 2, x, y, minus, x, cubed, end fraction.
Write the equation of the vertical line that is tangent to the curve.