general form of the equation of a circle
TRANSCRIPT
GeneralFormoftheEquationofaCircle
TheGeneralFormofequationofacircle,
Toreducetheequation,divideeachtermbyA.
ToChangefromGeneralFormtoStandardForm
Step1.DivideeachtermbyA.
Step2.Transposetheconstanttermtotherightsideoftheequation.
Step3.Completerthesquareonxandony.
Step4.Factorontheleftandaddontheright.
Example1.Writeinstandardformandgraph:
ToChangefromGeneralFormtoStandardForm
Step1.DivideeachtermbyA.
Step2.Transposetheconstanttermtotherightsideoftheequation.
Step3.Completerthesquareonxandony.
Step4.Factorontheleftandaddontheright.
Example2.Writeinstandardformandgraph:
ToChangefromGeneralFormtoStandardForm
Step1.DivideeachtermbyA.
Step2.Transposetheconstanttermtotherightsideoftheequation.
Step3.Completerthesquareonxandony.
Step4.Factorontheleftandaddontheright.
Example2.Writeinstandardformandgraph:
SOLUTION:
0912422 =−−−+ yxyx This is the given equation.
( ) ( ) 9124 22 =−+− yyxx Rewrite in anticipation of completing the square.
( ) ( ) 3649361244 22 ++=+−++− yyxx Complete the square on xand on y.
Factor on the left and add on the right.( ) ( ) 4962 22 =−+− yx
Example2.Writeinstandardformandgraph:
CONTINUED:
( ) ( ) 222 762 =−+− yx
StandardFormoftheEquationofaCircle
( ) ( ) 222 rkyhx =−+−
This is with h = 2.
( )2hx − This is with k = 6.
( )2ky −
This is with r = 7.
2r
We use the center, (h, k) = (2, 6), and the radius, r = 7, to graph the circle. The graph is shown below.
( ) ( ) 4962 22 =−+− yx
-15-12
-9-6
-30
36
912
15
-15 -12 -9 -6 -3 0 3 6 9 12 15
(2,6)
7
7
7
7
3 items
Example3.Writeinstandardform,findthecenterandradiusofthecircleandgraph.
Example4.Writeinstandardform,findthecenterandradiusofthecircleandgraph.
2 2 8 7 0x y x+ − + =
Example5.Writeinstandardform,findthecenterandradiusofthecircleandgraph.
Example5.Writeinstandardform,findthecenterandradiusofthecircleandgraph.