Respuesta :
Answer:
2
Step-by-step explanation:
Given the circle: [tex]x^2 + y^2 - 4x - 4y + 4 = 0[/tex]
To determine the length of the radius, we complete the square.
Step 1: Subtract 4 from both sides
[tex]x^2 + y^2 - 4x - 4y + 4 -4= 0-4\\x^2 + y^2 - 4x - 4y = -4[/tex]
Step 2: Divide the coefficient of x and y by 2, square it and add it to both sides
[tex]x^2 - 4x+(-2)^2+ y^2 - 4y+(-2)^2 = -4+(-2)^2+(-2)^2[/tex]
Step 3: Factorize the Left Hand side and simplify the Right Hand side.
[tex](x-2)^2+ (y-2)^2 = 2^2[/tex]
Comparing with the standard form of the equation of a circle
[tex](x-h)^2+ (y-k)^2 = r^2[/tex]
r=2
Therefore, the radius of the circle is 2.
