Question

x² + y² + 26x - 22y + 279 = 0
(x + 13)² + (y - 11)² = 11
(x - 13)² + (y + 11)² = 121
(x + 11)² + (y + 14)² = 11
(x + 13)² + (y - 11)² = 121

Explanation:

Step1: Group x and y terms

$x^2 + 26x + y^2 - 22y = -279$

Step2: Complete the square for x

$x^2 + 26x + 13^2 = (x+13)^2$, add $13^2=169$

Step3: Complete the square for y

$y^2 -22y + 11^2=(y-11)^2$, add $11^2=121$

Step4: Add constants to RHS

$-279 + 169 + 121 = 11$

Step5: Write standard form

$(x+13)^2 + (y-11)^2 = 11$

Answer:

A. $(x + 13)^2 + (y - 11)^2 = 11$