College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 2 - Section 2.4 - Circles - 2.4 Assess Your Understanding: 14

Answer

Standard form: $\color{blue}{x^2+y^2=9}$ General form: $\color{magenta}{x^2+y^2-9=0}$ Refer to the image below for the graph.
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Work Step by Step

RECALL: The standard form of a circle's equation is: $(x-h)^2 +(y-k)^2=r^2$ where $r$ = radius and $(h, k)$ is the center. The circle has: center: $(h, k)=(0, 0)$ $r=3$ Substitute the given values of $h, k,$ and $r$ into the standard form above to obtain: $(x-0)^2+(y-0)^2=3^2 \\\color{blue}{x^2+y^2=9}$ Write the equation in general form by subtracting $9$ on both sides of the equation to obtain: $x^2+y^2=9 \\\color{magenta}{x^2+y^2-9=0}$ To graph the circle, perform the following steps: (1) Plot the center $(0, 0)$. (2) With a radius of $3$ units, plot the following points: 3 units to the left of the center: $(-3, 0)$ 3 units to the right of the center: $(3, 0)$ 3 units above the center: $(0, 3)$ 3 units below the center: $(0 ,-3)$ (3) Connect the four points above (not including the center) using a smooth curve to form a circle. (Refer to the attached image in the answer part above for the graph.)
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