Center And Radius X^2-4x+Y^2-4y-8=0

Center and radius x^2-4x+y^2-4y-8=0

 

Answer:

Center Radius Form:

(x - 2)² + (y - 2)² = 16  or  (x - 2)² + (y - 2)² = 4²

Center (h,k) = (2, 2)

Radius = 4

Step-by-step explanation:

Change to Radius-Center standard form by completing the square:

x² - 4x + y² - 4y - 8 = 0

x² - 4x + (4/2)² + y² - 4y + (4/2)² = 8 + (4/2)² + (4/2)²

x² - 4x +(2)² + y² - 4 + (2)² = 8 + (2)² + (2)²

(x - 2)² + (y - 2)² = 8 + 4 + 4

(x - 2)² + (y - 2)² = 16

Standard form:

(x - h)² + (y - k)² = r²

(x - 2)² + (y - 2)² = 16

Center (h, k) = (2, 2)

Radius ⇒ r²=16 ⇒ r  = √16 ⇒ r = 4