   Chapter 2.6, Problem 47E

Chapter
Section
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:

ddxxn=nxn-1

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,

x2+y2=r2

Differentiate with respect to x

ddxx2+y2=r2

2x+2ydydx

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