The Circle and Its The Circle and Its equationequation

Conic SectionConic Section

General EquationGeneral Equation

122 yxBasic Equation

Center(0,0) Radius=1

General Equation

Center(h,k) Radius=r

ExamplesExamples

(x-0)(x-0)22+(x-1)+(x-1)22=25=25

Center is at (0,1) with radius of 5Center is at (0,1) with radius of 5

Given Center and RadiusGiven Center and Radius

Center is (-6, 10) with radius of 4Center is (-6, 10) with radius of 4

(x+6)(x+6)22+(y-10)+(y-10)22=16=16

Given Center and a PointGiven Center and a Point

Distance formulaDistance formula

)()( 2121 yyxxr

Center at (xCenter at (x11,y,y11) ) Point on circle (xPoint on circle (x22,y,y22) )

ExampleExample

Center is at (3,-7) with a point of (7,-10)Center is at (3,-7) with a point of (7,-10)

(3-7)(3-7)22+(-7-(-10))+(-7-(-10))22

(-4)(-4)22+(3)+(3)22

16+916+9 =5 =5

Equation is

(x-3)2+(x+7)2=25

Try some on your ownTry some on your own

Find the center of the circle given the equationFind the center of the circle given the equation

49)12()9( 22 xx

(-9,12) (9,-12)

Example 2Example 2

Find the equation of a circle with center of Find the equation of a circle with center of (-3,7) and a radius of 8 (-3,7) and a radius of 8

(x-3)2+(x+7)2=64 (x-3)2+(x+7)2=8

(x+3)2+(x-7)2=8(x+3)2+(x-7)2=64

Example 3Example 3

Find the equation of a circle with a center of Find the equation of a circle with a center of (-4,5) and has the point (3, 6)(-4,5) and has the point (3, 6)

(x-4)2+(x-5)2=49

(x+4)2+(x-5)2=50(x+4)2+(x-5)2=48

(x-4)2+(x+5)2=50

SummarySummary

Equation of any circle is Equation of any circle is

(x-h)(x-h)22+(x-k)+(x-k)22=r=r22

Center is (h,k)Center is (h,k) Radius is rRadius is r

Distance FormulaDistance Formula

22 )()( ykxhr

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