The Circle and Its equation

Conic Section

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

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

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 (x1,y1) Point on circle (x2,y2)

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 16+9 =5

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

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

Back to Mr. Mowry’s web-site Summary Equation of any circle is (x-h)2+(x-k)2=r2 Center is (h,k) Radius is r Distance Formula Back to Mr. Mowry’s web-site