SOLUTION: Write the equation of the circle x^2+10x+y^2-6y+29=0 in standard form. Find the radius and center of the circle. More than an answer I need an explanation please. I have seen ho

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write the equation of the circle x^2+10x+y^2-6y+29=0 in standard form. Find the radius and center of the circle. More than an answer I need an explanation please. I have seen ho      Log On


   

Question 737637: Write the equation of the circle x^2+10x+y^2-6y+29=0 in standard form. Find the radius and center of the circle.
More than an answer I need an explanation please. I have seen how some people "complete the square", and I don't know how to do that.
Thank you in advance.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Write the equation of the circle x^2+10x+y^2-6y+29=0 in standard form. Find the radius and center of the circle.
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x%5E2%2B10x%2By%5E2-6y%2B29=0
x%5E2%2B10x+%2B+y%5E2-6y+=+-29
Complete the squares for x and y separately.
x%5E2%2B10x
In the form ax%5E2+%2B+bx+%2B+c, a = 1 & b = 10
Add c, c = (b/2a)^2
c = (10/2)^2 = 25
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y^2-6y
c = (-6/2)^2 = 9
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x%5E2%2B10x25+%2B+y%5E2-6y%2B9+=+-29+%2B+25+%2B+9
x%5E2%2B10x25+%2B+y%5E2-6y%2B9+=+5
%28x%2B5%29%5E2+%2B+%28y-3%29%5E2+=+5 is "Standard Form"
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5 = r^2 --> radius+=+sqrt%285%29
The center is (-5,3)