Find the equation of a circle given three points P1 (0,0), P2(0,4), and
P3(-4,0) on the circle.

Point 1 ( x , y )

Point 2 ( x , y )

Point 3 ( x , y )

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( x - )² + ( y - ) ² = r² ANSWER

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Center of the circle (h,k)

Answer, h or x =

Answer, k or y =

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radius of the circle, r

( - )² + ( - )² = r² , Using Point 1 coordinates.
The radius, r² =

The radius, r =

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Memory recall lesson learned about equation of a circle. Then memory recall lesson learned about binomial expansion.

Equation 1: ( - h )² + ( - k )² = r², Using Point 1.

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Binomial Expansion: - h + h² + - k + k² = r²

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Equation 2: ( - h )² + ( - k )² = r² , Using Point 2.

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Binomial Expansion: - h + h² + - k + k² = r²

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Equation 1, r² = Equation 2, r²

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- h + h² - k + k² = - h + h² - k + k²

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Equation 3, - h = k

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Equation 4: ( - h )² + ( - k )² = r², Using Point 3

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- h + h² - - k + k² = r²

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Equation 1, r² = Equation 4, r²

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- h + h² - k + k² = - h + h² - k + k²

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Equation 5, - h = k

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h + k = Equation 3

h + k = Equation 5

Memory recall lesson learned about two simultaneous equations to solve for the value of
h = and k =

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