The Circle and Its equation

Conic Section

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

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

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

Given Center and a Point Distance formula Center at (x 1,y 1 ) Point on circle (x 2,y 2 )

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

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

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

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

Summary Equation of any circle is (x-h) 2 +(x-k) 2 =r 2 Center is (h,k) Radius is r Distance Formula Back to Mr. Mowry’s web-site