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 - Page 186: 13


Standard Form of the equation: $\color{blue}{x^2+y^2=4}$ General Form: $\color{magenta}{x^2+y^2-4=0}$ (Refer to the image below for the graph.)

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: $(h, k)=(0, 0)$ $r=2$ Substitute the given values of $h, k,$ and $r$ into the standard form above to obtain: $(x-0)^2+(y-0)^2=2^2 \\\color{blue}{x^2+y^2=4}$ Write the equation in general form by subtracting $4$ on both sides of the equation to obtain: $x^2+y^2=4 \\\color{magenta}{x^2+y^2-4=0}$ To graph the circle, perform the following steps: (1) Plot the center $(0, 0)$. (2) With a radius of $2$ units, plot the following points: 2 units to the left of the center: $(-2, 0)$ 2 units to the right of the center: $(2, 0)$ 2 units above the center: $(0, 2)$ 2 units below the center: $(0 ,-2)$ (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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