# 3,000 Solved Problems in Calculus 26 - CHAPTER 4 Circles...

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CHAPTER4Circles4.1Writethestandard equationfor acircle with centerat(a, b)andradiusr.y the distance formula, a point (x, y) is on the circle if and only ifbothsides,weobtainthestandard equation:(xa)2+ (yb)2=r2.4.2Writethestandard equationfor thecircle withcenter(3,5)andradius4.4.3Writethestandard equationfor thecircle with center(4, -2) andradius7.4.4Writethestandard equationfor thecircle with centerat theoriginandradiusr.4.5Findthestandard equationof thecircle with centerat (1, -2) andpassing throughthepoint(7,4).
Completethesquareinxand iny:(x -6)2+(y +10)2+ 15 = 36 +100.[Herethe-6in(x -6) ishalfofthecoefficient,-12,ofxintheoriginalequation,andthe +10in(_y+ 10)ishalfof thecoefficient20, ofy.The 36 and 100 on theright balancethesquaresof -6 and +10thathaveineffectbeen addedon theleft.]Simplifying,we
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