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: 41


center: $(0, 0)$ 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 the origin and a radius of $r$ units is: $x^2+y^2=r^2$ The given equation can be written as $x^2+y^2=4^2$. This is the same form as the standard equation above, so its center must be at the origin and its radius must be 4. Thus: center: $(0, 0)$ radius = $4$ units To graph the equation, do the following steps: (1) Plot the center $(0, 0)$, and then locate the points four units to the left, to the right, above, and below the circle's center. These points are: $(-4, 0)$ $(4, 0)$ $(0, -4)$ $(0, 4)$ (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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