SOLUTION: Find the equation of the circle (standard form) with center at (3,-4) and passing through (-1,-4). (show your soution)

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Question 394955: Find the equation of the circle (standard form) with center at (3,-4) and passing through (-1,-4). (show your soution)
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Starting with the standard form for a circle of radius r and center at (h, k):
%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2
The center is given as (3, -4) so h = 3 and k = -4. Substitute.
%28x-3%29%5E2%2B%28y%2B4%29%5E2+=+r%5E2 Find r%5E2 by substituting the x- and y-coordinates of the given point and solving for r or use the distance formula to find the distance from the center (3, -4) to the point on the circle (-1, -4):d+=+sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29
%28x-3%29%5E2%2B%28y%2B4%29%5E2+=+r%5E2 Substitute x = -1 and y = -4.
%28-1-3%29%5E2%2B%28-4%2B4%29%5E2+=+r%5E2 Evaluate.
%28-4%29%5E2+=+r%5E2
16+=+r%5E2
Final equation is:
%28x-3%29%5E2%2B%28y%2B4%29%5E2+=+16