SOLUTION: classify the conic section defined by thr equation. write the standard equation of the conic section: x^2+2x+y^2+6y+6=0

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Question 83341: classify the conic section defined by thr equation. write the standard equation of the conic section:
x^2+2x+y^2+6y+6=0
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B2x%2By%5E2%2B6y%2B6=0 Start with the given equation

x%5E2%2B2x%2By%5E2%2B6y=-6 Subtract 6 from both sides

%28x%5E2%2B2x%29%2B%28y%5E2%2B6y%29=-6 Group like terms

%28x%5E2%2B2x%2B2%29%2B%28y%5E2%2B6y%2B9%29=-6%2B2%2B9 Complete the square

%28x%5E2%2B2x%2B2%29%2B%28y%5E2%2B6y%2B9%29=5 Add

%28x%2B1%29%5E2%2B%28y%2B3%29%5E2=5 Factor

So the equation is a circle with a radius of sqrt%285%29 and a center of (-1,-3)