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Consider the equation .

  1. Show that  .

    Use implicit differentiation.

  2. Determine the -coordinate of each point on the curve where the tangent line is vertical.

    A tangent line will be vertical where the denominator of the derivative .

    Since the denominator has both and values, there will be infinitely many ways to make the denominator equal to .
    But only some (or one) of those ways fit the given curve.