Find the equation of a circle given three points P1 (0,0), P2(0,4), and
P3(-4,0) on the circle. Sometimes this calculator is not valid. Go to Geogebra interactive software shown below.

Point 1 ( x , y )

Point 2 ( x , y )

Point 3 ( x , y )

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( x - )² + ( y - ) ² = r² ANSWER EQUATION OF A CIRCLE.

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Find the coordinates of the center of circle (h,k)

Answer, h or x =

Answer, k or y =

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Find the radius of the circle, r

( - )² + ( - )² = r² , Using given Point 1 coordinates which is P1(0,0).
The radius, r² =

The radius, r =

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Memory recall lesson learned about equation of a circle. Equation 1

Equation 1: ( - h )² + ( - k )² = r², Using given Point 1 which is P1(0,0).

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Memory recall lesson learned about binomial expansion. Equation 1

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

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Equation 2: ( - h )² + ( - k )² = r² , Using given Point 2 which is P2(0,4).

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

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Radius of Equation 1, r² = Radius of Equation 2, r²

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- h + h² - k + k² = - h + h² - k + k²

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Equation 3 is derived by simplifying the above equation. - h = k

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Equation 4: ( - h )² + ( - k )² = r², Using given Point 3 which is P3(-4,0)

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Do the Binomial Expansion - h + h² - - k + k² = r²

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Radius of Equation 1, r² = Radius of Equation 4, r²

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- h + h² - k + k² = - h + h² - k + k²

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Equation 5 is derived by simplifying the above equation. - 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 = ?

Finally substitute the value of h and y in circle generalized equation

which is (x-h) ² + (y-k) ² = r ²

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Another method to find the equation of a circle is by using Geogebra software

Step 1. Write the three points

Step 2. Select Circle Icon - Tab

Step 3. Select circle through 3 points

Step 4. Select three points, the circle equation will be displayed

created by Apolinario "Sam" Ortega using Geogebra

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