Question

1. Dê as coordenadas do centro e o raio das circunferências representadas pelas equações;
a) x2 + y2 – 4x – 8y +16 = 0

Answer 1

$(x-a)^2+(y-b)^2=r^2\\\\ x^2+y^2-2ax-2by+a^2+b^2-r^2=0$

$-2a=-4\\\\ a=\frac{-4}{-2}\\\\ \boxed{a=2}\\\\ -2b=-8\\\\ b=\frac{-8}{-2}\\\\ \boxed{b=4}$

$a^2+b^2-r^2=16\\\\ 2^2+4^2-r^2=16\\\\ 4+16-r^2=16\\\\ -r^2=-4\\\\ r^2=4\\\\ r=\sqrt{4}\\\\ \boxed{r=2}$

$C(2,4)\\\\\ r=2$