Question

A) escreva a equação das circunferências de centro C e raio r nos seguintes casos :

B) determine o centro e o raio das circunferências definidas pelas equações seguintes: ​

Answer 1

$\boxed{\begin{array}{l}\rm A)\\\tt a)~\sf (x-1)^2+(y+2)^2=9\\\tt b)~\sf (x+2)^2+(y-4)^2=25\\\tt c)~\sf (x+5)^2+y^2=25\\\tt d)~\sf\bigg(x-\dfrac{5}{2}\bigg)^2+(y-3)^2=36\\\tt e)~\sf(x+2)^2+(y-1)^2=1\\\tt f)~\sf(x+1)^2+\bigg(y-\dfrac{3}{2}\bigg)^2=\dfrac{13}{4}\end{array}}$

$\boxed{\begin{array}{l}\rm B)\\\tt a)~\sf x^2+y^2-2x+4y+1=0\\\sf x^2-2x+1+y^2+4y+4=-1+1+4 \\\sf r^2=4\implies r=\sqrt{4}=2\\\tt b)~\sf x^2+y^2-2x-4y-4=0\\\sf x^2-2x+1+y^2-4y+4=1+4+4\\\sf r^2=9\implies r=\sqrt{9}=3\\\tt c) 4x^2+4y^2-4x-4y+1=0\div(4)\\\sf x^2+y^2-x-y+\dfrac{1}{4}=0\\\\\sf x^2-x+\dfrac{1}{4}+y^2-y+\dfrac{1}{4}=\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{4}\\\\\sf r^2=\dfrac{1}{4}\implies r=\dfrac{1}{2}\\\tt d)~\sf2x^2+2y^2-4x-4y+1=0\div2\\\sf x^2+y^2-2x-2y+\dfrac{1}{2}=0\\\sf x^2-2x+1+y^2-2y+1=1+1-\dfrac{1}{2}\\\sf r^2=\dfrac{3}{2}\implies r=\dfrac{\sqrt{6}}{2}\end{array}}$