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Lena [83]
3 years ago
14

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

Mathematics
1 answer:
MakcuM [25]3 years ago
7 0

Answer:

2

Step-by-step 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.

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