Problems from Circumference that goes through 3 given points

Find the circumference that goes through points $a = (2, 0)$ , $b = (2, 3)$ and $c = (1, 3)$ .

See development and solution

Development:

We replace them in the general equation of the circumference $x^{2} + y^{2} + A x + B y + C = 0$ . Thereby we obtain:

${\begin{matrix} 2^{2} + 0 + 2 A + 0 + C = 0 \\ 2^{2} + 3^{2} + 2 A + 3 B + C = 0 \\ 1^{2} + 3^{2} + A + 3 B + C = 0 \end{matrix}} \Rightarrow {\begin{matrix} 4 + 2 A = - C \\ 13 + 2 A + 3 B + C = 0 \\ 10 + A + 3 B + C = 0 \end{matrix}$ We solve the system and get: ${\begin{matrix} A = - 3 \\ B = - 3 \\ C = 2 \end{matrix}$ And we have the equation $x^{2} + y^{2} - 3 x - 3 y + 2 = 0$

Solution:

$x^{2} + y^{2} - 3 x - 3 y + 2 = 0$

Hide solution and development