##
Implicit Differentiation - Exercise 2

**Exercise 2.** Prove that an equation of the tangent line to
the graph of the hyperbola

at the point
*P*(*x*_{0},*y*_{0}) is

**Answer.** Instead of finding *y* explicitly as a function of
*x*, we will use implicit differentiation to find the slope of
the tangent line. We have

or equivalently

So the equation of the tangent line at the point
*P*(*x*_{0},*y*_{0}) is

or equivalently

Knowing that

the equation of the tangent line becomes

**
**

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