section 9-2 graphing circles 1 general form for a circle represents the center of the circle...
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3 We need to complete the square, collect terms, get constant by itself Now to complete the square divided 6 by 2 and square, divide -4 by 2 and square Add the same to the other side of the = sign Write as quantity’s squaredTRANSCRIPT
Section 9-2 GraphingCircles
11
222 )()( rkyhx
),( kh
),( yx
r
222 )()( ryx
General form for a circle
Represents the center of the circle
Represents a point on the circle
Represents the radius of the circle
General form for a circle centered at the origin
Example: Graph the following equation
22
9)2()3( 22 yx
)2,3(center 3radius
Example: Graph the following equation
33
0124622 yxyx
1246 22 yyxx
49124496 22 yyxx
2523 22 yx
)2,3(center
5radius
We need to complete the square, collect terms, get constant by itself
Now to complete the square divided 6 by 2 and square, divide -4 by 2 and square
Add the same to the other side of the = sign
Write as quantity’s squared
Example: Graph the following equation
44
0581022 yxyx
5810 22 yyxx
162551682510 22 yyxx
3645 22 yx
)4,5( center
6radius
We need to complete the square, collect terms, get constant by itself
Now to complete the square divided -10 by 2 and square, divide 8 by 2 and square
Add the same to the other side of the = sign
Write as quantity’s squared
Example: Graph the following equation
55
05422 xyx
54 22 yxx
4544 22 yxx
92 22 yx
)0,2(center
3radius
We need to complete the square, collect terms, get constant by itself
Now to complete the square divided 4 by 2 and square
Add the same to the other side of the = sign
Write as quantity’s squared
We can also write the equation for a circle if we know a point and the center all we need is the general form.
Example: write the equation of the circle with the following information: Center Point
66
222 )()( rkyhx )5,7( )2,3(
222 )7()4( r
Plugging in the values we can solve for r2 and plug the center and r2 into the general form again
Using this value we can write our equation
222 )52()73( r
24916 r265 r
65)5()7( 22 yx
We can also write the equation for a circle if we know a point and the center all we need is the general form.
Example: write the equation of the circle with the following information: Center Point
77
222 )()( rkyhx )2,9( )0,0(
222 )2()9( r
Plugging in the values we can solve for r2 and plug the center and r2 into the general form again
Using this value we can write our equation
222 )20()90( r
2481 r285 r
85)2()9( 22 yx
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