What’s the correct answer for this?

Option (2)

Step-by-step explanation:

Equation of the circle has been given as x² + 12y + 22x + y²- 167 = 0

Now we will convert this equation into the standard equation of the circle.

x² + 12y + 22x + y² - 167 = 0

(x² + 22x) + (y² + 12y) = 167

[x² + 2(11)x] + [y² + 2(6y)] = 167

[x² + 2(11)x + (11)²- (11)²] + [y² + 2(6)y + (6)²- (6)²] = 167

[x² + 1(11)x + (11)²] - (11)² +[y² + 2(6)y + 6²] - (6)² = 167

(x + 11)² + (y + 6)²- (11)²- (6)² = 167

(x + 11)² + (y + 6)² - 121 - 36 = 167

(x + 11)² + (y + 6)² - 157 = 167

(x + 11)² + (y + 6)²- 157 + 157 = 167 + 157

(x + 11)² + (y + 6)² = 324

Therefore, option (2) will be the standard equation of the given circle.