SOLUTION: A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the radius?

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Question 874597: A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the radius?
Answer by reviewermath(1029) About Me  (Show Source):
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Q:
A circle is described by the equation x%5E2+%2B+y%5E2+%2B+14x+%2B+2y+%2B+14+=+0. What are the coordinates for the center of the circle and the length of the radius?
A:
Express the equation in the form %28x+-+h%29%5E2+%2B+%28y+-+k%29%5E2+=+r%5E2.
x%5E2+%2B+y%5E2+%2B+14x+%2B+2y+%2B+14+=+0
%28x%5E2++%2B+14x%29+%2B+%28y%5E2+%2B+2y%29+=+-14
%28x%5E2++%2B+14x+%2B+49%29+%2B+%28y%5E2+%2B+2y+%2B+1%29+=+-14+%2B+49+%2B+1
%28x+%2B+7%29%5E2+%2B+%28y+%2B+1%29%5E2+=+36
h = -7, k = -1, and r = sqrt%2836%29 = 6
Therefore, the center is (-7, -1) and the length of the radius is 6.