Resposta:
Bom dia
Explicação passo-a-passo:
Vamos lá! Buscaremos o raio calculando a distância da reta ao centro:
[tex]|d_{(raio)}| =\dfrac{3\centerdot1+1\centerdot2-9}{\sqrt{3^2+11^2} } \\\\\\|d_{(raio)}| =\dfrac{3+2-9}{\sqrt{9+1} } \\\\\\d_{(raio)} =|\dfrac{-4}{\sqrt{10} } |\\\\\\d_{(raio)} =\boxed{\dfrac{4}{\sqrt{10} }}[/tex]
Aplicando as propriedades, temos:
[tex]Centro:(1;\ 2)\\\\(x - a)^{2} + ( y - b)^{2} = r^{2} \\\\\\Equacao-Reduzida\\(x - 1)^{2} + ( y -2)^{2} = r^{2}\\\\(x - 1)^{2} + ( y -2)^{2} =(\dfrac{4}{\sqrt{10} })^{2}\\\\(x - 1)^{2} + ( y -2)^{2} =\dfrac{16}{{10} } \\\\\boxed{(x - 1)^{2} + ( y -2)^{2} =1,6}[/tex]
[tex]Aplicando\ os\ Produtos\ notaveis\\(x -1)^{2} =x^{2} -2x+1\\\\( y -2)^{2} = y^{2} -4y+4\\\\x^{2} -2x+1+ y^{2} -4y+4=1,6\\\\x^{2} + y^{2} -2x-4y+5-1,6=0 \\\\Equacao-Geral:\\\boxed{x^{2} + y^{2} -2x-4y+3,4=0}\\[/tex]
Bons estudos!!!
