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2X² + 2Y² + 8X = -7; Divido toda expresion por 2
X² + Y² + 4X = -7/2
X² + 4X = X² + 4X + 4 - 4
X² + 4X + 4 = (X + 2)²
X² + 4X = (X + 2)² - 4;
Y² = (Y + 0)²
(X + 2)² - 4 + (Y + 0)² = -7/2
(X + 2)² + (Y + 0)² = -7/2 + 4
(X + 2)² + (Y + 0)² = 1/2
(X - h)² + (Y - k)² = r²;
- h = 2; h = -2; k = 0
r² = 1/2;
Entonces La circunferencia tiene centro en (-2,0) y radio r= \sqrt{1/2}
Te anexo la grafica