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Equation of a circle given three points
Find the equation of a circle given three points P1 (0,0), P2(0,4), and
P3(-4,0) around the circle
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Point 1 ( x , y )
Point 2 ( x , y )
Point 3 ( x , y )
( x - )2 + ( y - ) 2 = ANSWER
Equation 1: ( - h )2 + ( - k )2 = r2, Using Point 1.
Binomial Expansion: - h + h2 + - k + k2 = r2
Equation 2: ( - h )2 + ( - k )2 = r2 , Using Point 2.
Binomial Expansion: - h + h2 + - k + k2 = r2
Equation 1, r2 = Equation 2, r2
- h + h2 - k + k2 = - h + h2 - k + k2
Equation 3, - h = k
Equation 4: ( - h )2 + ( - k )2 = r2, Using Point 3
- h + h2 - - k + k2 = r2
Equation 1, r2 = Equation 4, r2
- h + h2 - k + k2 = - h + h2 - k + k2
Equation 5, - h = k
h + k = Equation 3
h + k = Equation 5
Center of the circle (h,k)
Answer, h =
Answer, k =
radius of the circle, r
( - )2 + ( - )2 = r2 , Using Point 1 coordinates.
The radius, r2 =