Question

RESOLUÇÃO!
Qual das seguintes retas passa pelo centro da circunferência x2 + y2 + 4y - 3 = 0? a) x + 2y = 4.
b) 5x – y = 2.
c) x + y = 0.
d) x – 5y = –2.
e) 2x + y = 7.

Answer 1

$\mathrm{x^2+y^2+4y-3=0\ \to\ x^2+y^2+4y=3}\\ \mathrm{x^2+(y^2+4y+4)=3+4\ \to\ (x-0)^2+(y+2)^2=7}\\\\ \mathrm{\Rightarrow Centro\ \to\ C(x_C,y_C)=C(0,-2)}\\\\ \mathrm{a)\ x+2y=4\ \to\ 0+2y=4\ \to\ y=2\ \to\ incorreto}\\ \mathrm{b)\ 5x-y=2\ \to\ 5.0-y=2\ \to\ y=-2\ \to\ correto}\\\\ \mathbf{Alternativa\ B.}$