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Consider the curve formed by the equation .

  1. Show that .

    Use implicit differentiation.

  2. Find 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 = 0.

    Since the denominator has both x and y values, there will be infinitely many ways to make the denominator equal to 0.
    But only some (or one) of those ways fit the given curve.