Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 13 - Conic Sections - 13.1 Conic Sections: Parabolas and Circles - 13.1 Exercise Set: 44

Answer

$(x+1)^2+(y+3)^2=34$

Work Step by Step

Using $(x-h)^2+(y-k)^2=r^2$ or the Center-Radius form of the equation of circles, the equation of the circle with center $( -1,-3 )$ is \begin{array}{l}\require{cancel} (x-(-1))^2+(y-(-3))^2=r^2 \\\\ (x+1)^2+(y+3)^2=r^2 .\end{array} Since the given point, $( -4,2 ),$ is on the circle, then substitute these coordinates into the $x$ and $y$ variables, respectively, of the equation above. \begin{array}{l}\require{cancel} (-4+1)^2+(2+3)^2=r^2 \\\\ (-3)^2+(5)^2=r^2 \\\\ 9+25=r^2 \\\\ r^2=34 .\end{array} Using the given center and the solved radius, the equation of the circle is $ (x+1)^2+(y+3)^2=34 .$
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