76.4k views
0 votes
What is the length of a radius of the circle represented by the equation below?

x2 + y2 - 4x – 4y + 4 = 0?

User Stepaklots
by
8.6k points

1 Answer

7 votes

Answer:

2

Explanation:

Given the circle:
x^2 + y^2 - 4x - 4y + 4 = 0

To determine the length of the radius, we complete the square.

Step 1: Subtract 4 from both sides


x^2 + y^2 - 4x - 4y + 4 -4= 0-4\\x^2 + y^2 - 4x - 4y = -4

Step 2: Divide the coefficient of x and y by 2, square it and add it to both sides


x^2 - 4x+(-2)^2+ y^2 - 4y+(-2)^2 = -4+(-2)^2+(-2)^2

Step 3: Factorize the Left Hand side and simplify the Right Hand side.


(x-2)^2+ (y-2)^2 = 2^2

Comparing with the standard form of the equation of a circle


(x-h)^2+ (y-k)^2 = r^2

r=2

Therefore, the radius of the circle is 2.

User Daveyfaherty
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories