Answer:
(x - 9)² + (y - 7)² = 262
Explanation:
x² + y² - 18x - 14y - 132 = 0
Rearranging the equation:
y² - 14y + x² - 18x - 132 = 0
add 132 to both sides:
y² -14y + x² - 18x - 132 + 132 = 0 + 132
y² -14y + x² - 18x = 132
add to both sides the square of half of the coefficient of y (i.e (14/2)² = 49)
y² -14y + 49 + x² - 18x = 132 + 49
add to both sides the square of half of the coefficient of x (i.e (18/2)² = 81)
y² -14y + 49 + x² - 18x + 81 = 132 + 49 + 81
y² -14y + 49 - x² - 18x - 81 = 262
y² - 7y - 7y + 49 + x² - 9x - 9x - 81 = 262
y(y - 7) - 7(y - 7) + x (x - 9) -9(x - 9) = 262
(y - 7)(y - 7) + (x - 9)(x - 9) = 262
(y - 7)²+ (x - 9)² = 262
(x - 9)² + (y - 7)² = 262