How to use implicit differentiation to find the equation of a tangent to a hyperbola.

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This video shows how implicit differentiation can be used to find the equation of a tangent line at a point on a hyperbola.

Error noted: The second last line should read y= (5/3)x - (16/3), though the final answer is correct.
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I tried to graph this in my calculator as done here, but the line I got was too far to the left of the right half of the hyperbole to be tangential to anything. Am I wrong or are you?

jesuisravi