x² + 6x+ y² + 8y = 11 . Complete the square of (x² + 6x) and (y² + 8y)
a) (x² + 6x) = x²+6x+9- 9 →(x+3)² - 9
b) (y² + 8y) = y²+8y+16-16→(y+4)² - 16
Result: (x+3)² - 9 + (y+4)² - 16 = 11
(x+3)² + (y+4)² - 25 = 11
(x+3)² + (y+4)² = 36 and the center O(-3,-4)