Equation of a circle passing through 3 points (x1, y1) (x2, y2) and (x3, y3).
The equation of the circle is described by the equation:
After substituting the three given points which lies on the circle we get the set of equations that can be described by the determinant:
The coefficienta A, B, C and D can be found by solving the following determinants:
The values of A, B, C and D will be after solving the determinants:
Center point (x, y) and the radius of a circle passing through 3 points (x1, y1) (x2, y2) and (x3, y3) are:
Example: Find the equation of a circle passing through the points (? 3, 4), (4, 5) and (1, ? 4).
A = ? 3(5 ? 4) ? 4(4 ? 1) ? 4(? 4) ? 1 ? 5 = ? 60
B = (9 ? 16)(? 4 ? 5) ? (16 ? 25)(4 ? 4) ? (1 ? 16)(5 ? 4) = 120
C = (9 ? 16)(4 ? 1) ? (16 ? 25)(1 ? 3) ? (1 ? 16)(? 3 ? 4) = 120
D = (9 ? 16)(1 ? 5 ? 4(? 4)) ? (16 ? 25)(? 3 ? (? 4) ? 1 · 4) ? (1 ? 16)(4 ? 4 ? (? 3)5) = 1380
Divide all terms by ? 60 to obtaine:
The center of the circle is by solving x and y is at point (1, 1)
The radius of the circle is:
The
equation of the circle represented by standard form is:
