Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\mathsf{d_{AB} = \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2}}[/tex]
[tex]\mathsf{d_{AB} = \sqrt{(1 - (-5))^2 + (4 - 2)^2}}[/tex]
[tex]\mathsf{d_{AB} = \sqrt{(1 + 5)^2 + (4 - 2)^2}}[/tex]
[tex]\mathsf{d_{AB} = \sqrt{(6)^2 + (2)^2}}[/tex]
[tex]\mathsf{d_{AB} = \sqrt{36 + 4}}[/tex]
[tex]\mathsf{d_{AB} = \sqrt{40}}[/tex]
[tex]\mathsf{d_{AB} = \sqrt{2^2.10}}[/tex]
[tex]\mathsf{d_{AB} = 2\sqrt{10}}[/tex]
[tex]\mathsf{r = \dfrac{d_{AB}}{2}}[/tex]
[tex]\mathsf{r = \dfrac{\not2\sqrt{10}}{\not2}}[/tex]
[tex]\boxed{\boxed{\mathsf{r = \sqrt{10}}}}\leftarrow\textsf{raio da circunfer{\^e}ncia}[/tex]
[tex]\mathsf{M_{AB} = \{\dfrac{x_A + x_B}{2};\dfrac{y_A + y_B}{2}\}}[/tex]
[tex]\mathsf{M_{AB} = \{\dfrac{-5 + 1}{2};\dfrac{2 + 4}{2}\}}[/tex]
[tex]\mathsf{M_{AB} = \{\dfrac{-4}{2};\dfrac{6}{2}\}}[/tex]
[tex]\boxed{\boxed{\mathsf{M_{AB} = \{-2;3\}}}}\leftarrow\textsf{centro da circunfer{\^e}ncia}[/tex]
[tex]\mathsf{(x - a)^2 + (y - b)^2 = R}^2}[/tex]
[tex]\mathsf{(x - (-2))^2 + (y - 3)^2 = (\sqrt{10})^2}[/tex]
[tex]\boxed{\boxed{\mathsf{(x + 2)^2 + (y - 3)^2 = 10}}}\leftarrow\textsf{equa{\c c}{\~a}o reduzida da circunfer{\^e}ncia}[/tex]
