Question

O diâmetro da circunferência de equação x2 + y2 + 4x - 6y + 10 = 0 é:

Answer 1

$\boxed{\begin{array}{l}\sf x^2+y^2+4x-6y+10=0\\\sf x^2+4x+\boxed{}+y^2-6y+\boxed{}=\boxed{}+\boxed{}-10\\\sf x^2+4x+\boxed{\sf\bigg(\dfrac{4}{2}\bigg)^2}+y^2-6y+\boxed{\sf\bigg(\sf\dfrac{6}{2}\bigg)^2}=\boxed{\bigg(\sf\dfrac{4}{2}\bigg)^2}+\boxed{\bigg(\sf\dfrac{6}{2}\bigg)^2}-10\\\\\sf x^2+4x+2^2+y^2-6y+3^2=2^2+3^2-10\\\sf (x+2)^2+(y-3)^2=4+9-10\\\sf (x+2)^2+(y-3)^2=3\\\sf R^2=3\\\sf R=\sqrt{3}\\\sf D=2\cdot R\\\sf D=2\sqrt{3}\end{array}}$