   Chapter 10.4, Problem 32E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Consider the circle with center ( h , k ) and radius length r . If the circle contains the point ( c , d ) , find the slope of the tangent line to the circle at the point ( c , d ) .

To determine

To find:

The slope of the tangent line to the circle at the point c, d and center at h, k.

Explanation

The Circle with centre (h,k) and point (c,d).

The above figure is circle with centre (h,k) and point (c,d) and the tangent line PQ.

Formula for slope of the radius is m1=y2-y1x2-x1

Where, x1, y1=(h,k)

And x2, y2=(c,d)

Substituting the above values in the formula as below,

Slope m1=d-kc-h

Hence the slope of the radius is m1=d-kc-h

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