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: 48

Answer

Center: $(-4, -5)$ Radius = $6$ units

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 $(x+4)^2+(y+5)^2=6^2$. This is the same form as the standard equation above, so its center must be at the point $(-4, -5)$ and its radius must be $6$. Thus, the circle has: center: $(-4, -5)$ radius = $6$ units To graph the equation, do the following steps: (1) Plot the center $(-4, -5)$, and then locate the points 6 units to the left, to the right, above, and below the circle's center. These points are: $(-10, -5) \\(2, -5) \\(-4, 1) \\(-4, -11)$ (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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