What is the length of a radius of the circle represented by the equation

x2 + y2 - 4x - 4y + 4 = 0?

A) 2 units

B) 4 units

C) 8 units

D) 16 units

A) 2 units

Step-by-step 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