Question

Obtenha o raio e o centro das circunferências a seguir:

a) x²+y²-6x=0
b) x²+y²-4x-8y+16=0
c) x²+y²-4y=0
d) x²+y²-2x-2y=0​

Answer 1

$a) x^2+y^2-6x=0\\\left(x-3\right)^2+\left(y-0\right)^2=3^2\\\\\left(a,\:b\right)=\left(3,\:0\right),\:r=3\\\\b) x^2+y^2-4x-8y+16=0\\\\\left(x-2\right)^2+\left(y-4\right)^2=2^2\\\\\left(a,\:b\right)=\left(2,\:4\right),\:r=2$

$c) x^2+y^2-4y=0\\\\\frac{\left(x-0\right)^2}{2^2}+\frac{\left(y-2\right)^2}{2^2}=1\\\\\left(h,\:k\right)=\left(0,\:2\right),\:a=2,\:b=2\\\\d) x^2+y^2-2x-2y=0\\\\\left(x-1\right)^2+\left(y-1\right)^2=\left(\sqrt{2}\right)^2\\\\\left(a,\:b\right)=\left(1,\:1\right),\:r=\sqrt{2}$