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.