Question

A equação da circunferência de centro no ponto c (1,2) e que passa no ponto p (-1;5) e é:
a) x² + y² + 2x + 4y=44
b) x² + y² + 2x - 4y= 4
c) x² + y² - 2x + 4y = 48
d) x² +y²- 2x - 4y = 8
e) x² + y² - x - y = 22

Answer 1

$\large\boxed{\begin{array}{l}\underline{\sf C\acute alculo\,do\,raio}\\\rm r=d_{c,p}\\\rm r=\sqrt{(x_p-x_c)^2+(y_p-y_c)^2}\\\rm r=\sqrt{(-1-1)^2+(5-2)^2}\\\rm r=\sqrt{4+9}\\\rm r=\sqrt{13}\longrightarrow r^2=13\\\rm (x-1)^2+(y-2)^2=13\\\rm x^2-2x+1+y^2-4y+4=13\\\rm x^2+y^2-2x-4y=13-1-4\\\rm x^2+y^2-2x-4y=8\\\huge\boxed{\boxed{\boxed{\boxed{\rm\dagger\red{\maltese}~\blue{alternativa~d}}}}}\end{array}}$