Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 10 - Section 10.1 - Distance and Midpoint Formulas; Circles - Exercise Set - Page 765: 44


center: $(2, 3)$ radius = $4$ 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 $(x-2)^2+(y-3)^2=4^2$. This is the same form as the standard equation above, so its center must be at the point $(2,3)$ and its radius must be 4. Thus, the circle has: center: $(2, 3)$ radius = $4$ units To graph the equation, do the following steps: (1) Plot the center $(2, 3)$, and then locate the points 4 units to the left, to the right, above, and below the circle's center. These points are: $(2,7)$ $(2,-1)$ $(6,3)$ $(-2, 3)$ (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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