1. The Circle and Its equation

2. Conic Section

3. General Equation Basic Equation Center(0,0) Radius=1 General Equation
Center(h,k) Radius=r

4. Center is at (0,1) with radius of 5
Examples
(x-0)2+(x-1)2=25
Center is at (0,1) with radius of 5

5. Given Center and Radius
Center is (-6, 10) with radius of 4
(x+6)2+(y-10)2=16

6. Given Center and a Point
Distance formula
Center at (x1,y1)
Point on circle (x2,y2)

7. Example Center is at (3,-7) with a point of (7,-10) (3-7)2+(-7-(-10))2
Equation is
(x-3)2+(x+7)2=25
(-4)2+(3)2 =5

8. Try some on your own Find the center of the circle given the equation
(9,-12)
(-9,12)

9. Example 2
Find the equation of a circle with center of (-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=64
(x+3)2+(x-7)2=8

10. Example 3
Find the equation of a circle with a center of (-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

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Summary
Equation of any circle is
(x-h)2+(x-k)2=r2
Center is (h,k)
Radius is r
Distance Formula
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