SOLUTION: Write the equation of a circle that passes through (7,-1) and has its center at (-2,4).

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Question 636105: Write the equation of a circle that passes through (7,-1) and has its center at (-2,4).
Found 2 solutions by jim_thompson5910, solver91311:
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--2%29%5E2%2B%28y-4%29%5E2=r%5E2 Plug in h=-2 and k=4 (since the center is the point (h,k) ).


%287--2%29%5E2%2B%28-1-4%29%5E2=r%5E2 Plug in x=7 and y=-1 (this is the point that lies on the circle, which is in the form (x,y) ).


%289%29%5E2%2B%28-5%29%5E2=r%5E2 Combine like terms.


81%2B25=r%5E2 Square each term.


106=r%5E2 Add.


So because h=-2, k=4, and r%5E2=106, this means that the equation of the circle with center (-2,4) that goes through the point (7,-1) is


%28x%2B2%29%5E2%2B%28y-4%29%5E2=106.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The distance from the center of a circle to a point on the circle is the radius. So use the distance formula



where and are the coordinates of the given points to determine the radius, then use the standard form of an equation of a circle centered at with radius to write your desired equation:



John

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