SOLUTION: Find the equation of a circle given its center C and one point P. C(0,4),P(0,0). Thank You!

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Question 530466: Find the equation of a circle given its center C and one point P.
C(0,4),P(0,0).
Thank You!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 Start with the general equation of a circle.


%28x-0%29%5E2%2B%28y-4%29%5E2=r%5E2 Plug in h=0 and k=4 (since the center is the point (h,k) ).


%280-0%29%5E2%2B%280-4%29%5E2=r%5E2 Plug in x=0 and y=0 (this is the point that lies on the circle, which is in the form (x,y) ).


%280%29%5E2%2B%28-4%29%5E2=r%5E2 Combine like terms.


0%2B16=r%5E2 Square each term.


16=r%5E2 Add.


So because h=0, k=4, and r%5E2=16, this means that the equation of the circle with center (0,4) that goes through the point (0,0) is


%28x-0%29%5E2%2B%28y-4%29%5E2=16.


which simplifies to


x%5E2%2B%28y-4%29%5E2=16


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