Question

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

Answer 1

Answer:

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