-
4.1ThestandardfromforanequationofacircleFILLEDINNOTES.notebookSeptember30,2014
4.1TheStandardFormForanEquationofaCircle
-
4.1ThestandardfromforanequationofacircleFILLEDINNOTES.notebookSeptember30,2014
Acircleisthesetofallpointsinaplaneatafixedpositivedistance(radius)fromafixedpoint(center)
Definition
Acirclewithcenter(h,k)andradiusrhasequation:(xh)2+(yk)2=r2
Theorem4.1
-
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
-
4.1ThestandardfromforanequationofacircleFILLEDINNOTES.notebookSeptember30,2014
Example1:Giveanequationforthecirclewithcenter(3,5)andradius2.Graphthiscircle.
-
4.1ThestandardfromforanequationofacircleFILLEDINNOTES.notebookSeptember30,2014
Example2:Express2x2+2y22x+6y3=0instandardform.
-
4.1ThestandardfromforanequationofacircleFILLEDINNOTES.notebookSeptember30,2014
-
4.1ThestandardfromforanequationofacircleFILLEDINNOTES.notebookSeptember30,2014
Example3:Expressx2+y2+4x6y+13=0instandardform,thensketchthegraph.
-
4.1ThestandardfromforanequationofacircleFILLEDINNOTES.notebookSeptember30,2014
Example4:Writetheequationofacircleingeneralformthathas(3,5)and(2,4)astheendpointsofthediameter.
-
4.1ThestandardfromforanequationofacircleFILLEDINNOTES.notebookSeptember30,2014
Example5:Findthepoint(s)ofintersectionofx2+y2+4x12y+6=0and3x5y+2=0.
-
4.1ThestandardfromforanequationofacircleFILLEDINNOTES.notebookSeptember30,2014
Page 1: Oct 4-7:49 PMPage 2: Oct 4-7:49 PMPage 3: Oct 4-7:49
PMPage 4: Oct 4-7:49 PMPage 5: Oct 4-7:49 PMPage 6: Sep 29-10:08
AMPage 7: Oct 4-7:49 PMPage 8: Oct 4-7:49 PMPage 9: Oct 4-7:49
PMPage 10: Sep 30-9:53 AM
