Show the complete steps to change - x^2 + y^2 - 18x - 14y - 132=0 to standard form.

(x - 9) ² + (y - 7) ² = 262

Step-by-step 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