SOLUTION: Write the standard equation of the circle passing through (2,5) with the center at (-2,-3). Sketh the graph.

Algebra ->  Linear-equations -> SOLUTION: Write the standard equation of the circle passing through (2,5) with the center at (-2,-3). Sketh the graph.      Log On


   

Question 204741: Write the standard equation of the circle passing through (2,5) with the center at (-2,-3). Sketh the graph.
Answer by alicealc(293) About Me  (Show Source):
You can put this solution on YOUR website!
the general equation of a circle with the center at (a, b) and radius r:
%28x+-+a%29%5E2+%2B+%28y+-+b%29%5E2+=+r%5E2

with the center at (-2, -3):
%28x+-+%28-2%29%29%5E2+%2B+%28y+-+%28-3%29%29%5E2+=+r%5E2
%28x+%2B+2%29%5E2+%2B+%28y+%2B+3%29%5E2+=+r%5E2
passing through (2, 5):
%282+%2B+2%29%5E2+%2B+%285+%2B+3%29%5E2+=+r%5E2
4%5E2+%2B+8%5E2+=+r%5E2
16+%2B+64+=+r%5E2
80+=+r%5E2

so,the standard equation is:
%28x+%2B+2%29%5E2+%2B+%28y+%2B+3%29%5E2+=+80
x%5E2+%2B+4x+%2B+4+%2B+y%5E2+%2B+6y+%2B+9+=+80
x%5E2+%2B+y%5E2+%2B+4x+%2B+6y+%2B+13+-+80+=+0
x%5E2+%2B+y%5E2+%2B+4x+%2B+6y+-+67+=+0

and the graph is: