## Intermediate Algebra for College Students (7th Edition)

Published by Pearson

# Chapter 10 - Section 10.1 - Distance and Midpoint Formulas; Circles - Exercise Set - Page 765: 43

#### Answer

center: $(3, 1)$ radius = $6$ units Refer to the image below for the graph.

#### Work Step by Step

RECALL: The standard form of the equation of a circle with a center at $(h, k)$ and a radius of $r$ units is: $(x-h)^2+(y-k)^2=r^2$ The given equation can be written as $(x-3)^2+(y-1)^2=6^2$. This is the same form as the standard equation above, so its center must be at the point $(3,1)$ and its radius must be 6. Thus, the circle has: center: $(3, 1)$ radius = $6$ units To graph the equation, do the following steps: (1) Plot the center $(3, 1)$, and then locate the points 6 units to the left, to the right, above, and below the circle's center. These points are: $(9, 1)$ $(-3, 1)$ $(3, 7)$ $(3, -5)$ (ii) Connect the four points (excluding the center) together using a curve to form a circle. (Please refer to the attached image in the answer part above.)

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