Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 1 - Graphs - 1.4 Circles - 1.4 Assess Your Understanding - Page 38: 36

Answer

Center (0, 2); radius = 2 No x-intercepts The y-intercepts are 4 and 0.

Work Step by Step

3x² + 3y² - 12y = 0 x² + y² - 4y = 0 Divide both sides by 3. x²+ (y² - 4y) = 0 x² + (y² - 4y + 4) = 0 + 4 Complete the square of each expression in parenthesis. x² + (y - 2)² = 4 x² + (y - 2)² = (2)² Compare this equation with the equation (x - h)² + (y - k)² = r². The comparison yields the information about the circle. We see that h = 0, k = 2 and r = 2. The circle has center (0, 2) and a radius of 2 units. To find the x-intercepts, if any, let y = 0 and solve for x. x² + (y - 2)² = ( 2)² x² + (0 -2)² = 4 x² + 4 = 4 x² + 4 - 4 = 4 - 4 Subtract 4 from both sides. x² = 0 x = 0 No x-intercepts. To find y-intercepts, if any, let x = 0 and solve for y. 0² + (y - 2)² = (2)² (y - 2)² = 4 y - 2 = ± 2 If y - 2 = 2 y - 2 + 2 = 2 + 2 y = 4 If y - 2 = - 2 y - 2 + 2 = - 2 + 2 y = 0 The y- intercepts are 4 and 0.
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