Chapter 2.6, Problem 47E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

Show, using implicit differentiation, that any tangent fine at a point *P* to a circle with center *O* is perpendicular to the radius *OP.*

To determine

**To show:**

Any tangent line at point P to a circle with center O is perpendicular to the radius OP.

Explanation

**1) Concept:**

Slope of the tangent line is a derivate of the curve at that point.

**2) Formula:**

**3) Calculations:**

Without loss of generality we may assume that the circle is centered at origin.

Let r be the radius of circle, then OP = r

Therefore, the equation circle under consideration is,

Differentiate with respect to x

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