Question

Help :D .......................

Answer 1

The circunference is represented by the equation is
`x^(2)+y^(2)-6\cdot x +4\cdot y +9=0`.

The graph of this function is presented in the attachment.

Explanation:

The general equation of the circunferece is defined by the following formula:

`x^(2)+y^(2)+A\cdot x + B\cdot y + C = 0` (1)

We can determine the value of the coefficients by knowing three distinct points:
`(x_(1), y_(1)) = (3,0)`,
`(x_(2),y_(2)) = (5,-2)`,
`(x_(3),y_(3)) = (1, -2)`

The system of linear equations is:

`3\cdot A + C = -9` (2)

`5\cdot A -2\cdot B + C = -29` (3)

`A -2\cdot B + C = -5` (4)

The solution of this system is:
`A = -6`,
`B = 4`,
`C = 9`.

The circunference is represented by the equation is
`x^(2)+y^(2)-6\cdot x +4\cdot y +9=0`.

The graph of this function is presented in the attachment.