Answer:
It's the first option.
Step-by-step explanation:
x^2 - 12x + 27 = - y^2 + 8y
x^2 - 12x + y^2 - 8y = -27 Completing the squares:
(x - 6)^2 - 36 + (y - 4)^2 - 16 = -27
(x - 6)^2 + (y - 4)^2 = -27 + 36 + 16
(x- 6)^2 + (y - 4)^2 = 25 is the standard equation.
The center is at (6, 4) and the radius is 5 units.
Answer:
first option
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² - 12x + 27 = - y² + 8y ( subtract - y² + 8y from both sides )
x² - 12x + y² - 8y + 27 = 0 ( subtract 27 from both sides )
x² - 12x + y² - 8y = - 27
Using the method of completing the square on both the x and y terms
add ( half the coefficient of the x/ y term )² to both sides
x² + 2(- 6)x + 36 + y² + 2(- 4)y + 16 = - 27 + 36 + 16
(x - 6)² + (y - 4)² = 25 ← in standard form
with centre = (6, 4 ) and r² = 25 ⇒ r = [tex]\sqrt{25}[/tex] = 5 → first option
