Answer:
x² + y² - 12x - 6y + 29 = 0
Step-by-step explanation:
Simplifying the equation using (a + b)² = a² + 2ab + b²:
(x - 6)² + (y - 3)² = 16
⇒ [x² - 2(x)(6) + 6²] + [y² - 2(y)(3) + 3²] = 16
⇒ [x² - 12x + 36] + [y² - 6y + 9] = 16
⇒ x² - 12x + 36 + y² - 6y + 9 = 16
General form of a circle = x² + y² + Cx + Dy + E = 0
Before we reorganize the equation in general form, we need to have the R.H.S as 0. For that, we need to subtract 16 both sides.
Subtract 16 both sides:
⇒ x² - 12x + 36 + y² - 6y + 9 = 16
⇒ x² - 12x + 36 + y² - 6y + 9 - 16 = 16 - 16
⇒ x² - 12x + 20 + y² - 6y + 9 = 0
Reorganizing the equation in general form:
x² - 12x + 20 + y² - 6y + 9 = 0
⇒ x² - 12x + 20 + y² - 6y + 9 = 0
⇒ x² + y² - 12x + 20 - 6y + 9 = 0
⇒ x² + y² - 12x + 20 - 6y + 9 = 0
⇒ x² + y² - 12x - 6y + 20 + 9 = 0
⇒ x² + y² - 12x - 6y + 29 = 0
Thus, the equation in general form is x² + y² - 12x - 6y + 29 = 0.
