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4.1ThestandardfromforanequationofacircleFILLEDINNOTES.notebookSeptember30,2014
4.1TheStandardFormForanEquationofaCircle
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4.1ThestandardfromforanequationofacircleFILLEDINNOTES.notebookSeptember30,2014
Acircleisthesetofallpointsinaplaneatafixedpositivedistance(radius)fromafixedpoint(center)
Definition
Acirclewithcenter(h,k)andradiusrhasequation:(xh)2+(yk)2=r2
Theorem4.1
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4.1ThestandardfromforanequationofacircleFILLEDINNOTES.notebookSeptember30,2014
Thinkofthedifferencebetweeny=mx+bandAx+By+C=0.Theslopeinterceptformreadilyshowsyoutheslopeandinterceptofthelinewhilethestandard,orgeneralform,isconsideredproper.Samegoesforcircles.While(xh)2+(hk)2=r2,thestandardform,readilygivesyouthecenterandradius,anotherform,thegeneralformispreferred.
Everycirclecanberepresentedinthegeneralform:Ax2+Ay2+Dx+Ey+F=0
Theorem4.2
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4.1ThestandardfromforanequationofacircleFILLEDINNOTES.notebookSeptember30,2014
Example1:Giveanequationforthecirclewithcenter(3,5)andradius2.Graphthiscircle.
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4.1ThestandardfromforanequationofacircleFILLEDINNOTES.notebookSeptember30,2014
Example2:Express2x2+2y22x+6y3=0instandardform.
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4.1ThestandardfromforanequationofacircleFILLEDINNOTES.notebookSeptember30,2014
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4.1ThestandardfromforanequationofacircleFILLEDINNOTES.notebookSeptember30,2014
Example3:Expressx2+y2+4x6y+13=0instandardform,thensketchthegraph.
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4.1ThestandardfromforanequationofacircleFILLEDINNOTES.notebookSeptember30,2014
Example4:Writetheequationofacircleingeneralformthathas(3,5)and(2,4)astheendpointsofthediameter.
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4.1ThestandardfromforanequationofacircleFILLEDINNOTES.notebookSeptember30,2014
Example5:Findthepoint(s)ofintersectionofx2+y2+4x12y+6=0and3x5y+2=0.
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4.1ThestandardfromforanequationofacircleFILLEDINNOTES.notebookSeptember30,2014
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