Answer:
The circunference is represented by the equation is [tex]x^{2}+y^{2}-6\cdot x +4\cdot y +9=0[/tex].
The graph of this function is presented in the attachment.
Step-by-step explanation:
The general equation of the circunferece is defined by the following formula:
[tex]x^{2}+y^{2}+A\cdot x + B\cdot y + C = 0[/tex] (1)
We can determine the value of the coefficients by knowing three distinct points: [tex](x_{1}, y_{1}) = (3,0)[/tex], [tex](x_{2},y_{2}) = (5,-2)[/tex], [tex](x_{3},y_{3}) = (1, -2)[/tex]
The system of linear equations is:
[tex]3\cdot A + C = -9[/tex] (2)
[tex]5\cdot A -2\cdot B + C = -29[/tex] (3)
[tex]A -2\cdot B + C = -5[/tex] (4)
The solution of this system is: [tex]A = -6[/tex], [tex]B = 4[/tex], [tex]C = 9[/tex].
The circunference is represented by the equation is [tex]x^{2}+y^{2}-6\cdot x +4\cdot y +9=0[/tex].
The graph of this function is presented in the attachment.
