The equation of the circle passing through the point a (0,5) B (1, - 2) C (- 3, - 4) is solved by the method of undetermined coefficient, and D E F is calculated first | Math enthusiast | Mathematical art

The equation of the circle passing through the point a (0,5) B (1, - 2) C (- 3, - 4) is solved by the method of undetermined coefficient, and D E F is calculated first

Let the circle be X & # 178; + Y & # 178; + DX + ey + F = 0
25+5E+F=0 (1)
1+4+D-2E+F=0 (2)
9+16-3D-4E+F=0 (3)
From (1)
F=-5E-25 (4)
(4) Substituting into (2), we get the following result:
D=2E-F-5=2E+5E+25-5=7E+20 (5)
(4) (5) substitute (3) to get:
25-3(7E+20)-4E-5E-25=0
E=-2
be
F=-15
D=6
Circle: X & # 178; + Y & # 178; + 6x-2y = 15

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