SOLUTION: find an equation a circle having a diameter whose endpoints are at (2,-1) and (6,-5)

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Question 968131: find an equation a circle having a diameter whose endpoints are at (2,-1) and (6,-5)
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
We need to find the equation of the circle that has its
center as the midpoint between (2,-1) and (6,-5), the green circle below:

 

Midpoint between (2,-1) and (6,-5), %28matrix%281%2C3%2C+++%282%2B6%29%2F2%2C%22%2C%22%2C%28-1%2B%28-5%29%29%2F2%29%29%22%22=%22%22%28matrix%281%2C3%2C+++8%2F2%2C%22%2C%22%2C%28-6%29%2F2%29%29 = (4,-3) 

and has its diameter as the distance between between (2,-1) and (6,-5)
and its radius as half that:

 

Therefore its center is (4,-3) and its
radius is one-half the diameter 2sqrt%282%29.

Its equation is

%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2

%28x-4%29%5E2%2B%28y-%28-3%29%29%5E2=%282sqrt%282%29%29%5E2

%28x-4%29%5E2%2B%28y%2B3%29%5E2=4%2A2

%28x-4%29%5E2%2B%28y%2B3%29%5E2=8

Or you can multiply it out and rearrange to get this:

x%5E2%2By%5E2-8x%2B6y%2B17+=+0

Edwin