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Tangent lines Find an equation of the line

Chapter 8, Problem 32RE

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QUESTION:

Tangent lines Find an equation of the line tangent to the following curves at the given point. Check your work with a graphing utility.

\(\frac{x^{2}}{16}-\frac{y^{2}}{9}=1 ;\left(\frac{20}{3},-4\right)\)

Questions & Answers

QUESTION:

Tangent lines Find an equation of the line tangent to the following curves at the given point. Check your work with a graphing utility.

\(\frac{x^{2}}{16}-\frac{y^{2}}{9}=1 ;\left(\frac{20}{3},-4\right)\)

ANSWER:

Solution 32RE

Step 1:

In this problem we have to find the equation of the line tangent to at the point

First let us find the slope of

Differentiate both sides with respect to x,

Therefore slope of is

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