SOLUTION: Write the general form of the equation of the circle with radius r and center (h, k). r = 2 ; (h, k) = (4, -4)

Algebra ->  Coordinate-system -> SOLUTION: Write the general form of the equation of the circle with radius r and center (h, k). r = 2 ; (h, k) = (4, -4)      Log On


   

Question 1063040: Write the general form of the equation of the circle with radius r and center (h, k). r = 2 ; (h, k) = (4, -4)
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
r = 2 ; (h, k) = (4, -4)
%28x-h%5E%22%22%29%5E2%2B%28y-k%5E%22%22%29%5E2%22%22=%22%22r%5E2

Substitute 4 for h, -4 for k, and 2 for r

%28x-4%5E%22%22%29%5E2%2B%28y-%28-4%29%5E%22%22%29%5E2%22%22=%22%222%5E2

Simplify,multiply everything out, collect terms, and get
0 on the right:

%28x-4%5E%22%22%29%5E2%2B%28y%2B4%5E%22%22%29%5E2%22%22=%22%224

%28x-4%5E%22%22%29%28x-4%5E%22%22%29%2B%28y%2B4%5E%22%22%29%28y%2B4%5E%22%22%29%22%22=%22%224

%28x%5E2-4x-4x%2B16%5E%22%22%29%2B%28y%5E2%2B4y%2B4y%2B16%29%22%22=%22%224

x%5E2-4x-4x%2B16%2By%5E2%2B4y%2B4y%2B16%22%22=%22%224

x%5E2-8x%2By%5E2%2B8y%2B32%22%22=%22%224

Get 0 on the right by subtracting 4 from both sides:

x%5E2-8x%2By%5E2%2B8y%2B28%22%22=%22%220

The general form has the squared terms first, then the
x and y terms then the constant (number), then = 0

x%5E2%2By%5E2-8x%2B8y%2B28%22%22=%22%220

Edwin