Answer:
A) 2 units
Explanation:
Given;
x² + y² - 4x - 4y + 4 = 0
Consider general circle equation;
(x - h)² + (y - k)² = r²
where;
(h , k ) is the center of the circle
r is the radius of the circle
x² + y² - 4x - 4y + 4 = 0
subtract 4 from both sides of the equation
x² + y² - 4x - 4y = - 4
square half of coefficient of x and y, and add them to both sides of the equation
x² + - 4x + (-2)² + y² - 4y + (-2)² = - 4 + (-2)² + (-2)²
factorize x and y
(x - 2)² + (y - 2)² = - 4 + 4 + 4
(x - 2)² + (y - 2)² = 4
(x - 2)² + (y - 2)² = 2²
Compare this final equation to general equation of a circle
(x - 2)² + (y - 2)² = 2²
(x - h)² + (y - k)² = r²
r = 2
Thus, the length of a radius of the circle is 2 units