SOLUTION: htis has to d with circles x^2+y^2+2x+4y=9

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Question 122945: htis has to d with circles
x^2+y^2+2x+4y=9
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

1x%5E2%2B2x%2B1y%5E2%2B4y-9=0 Start with the given equation


1x%5E2%2B2x%2B1y%5E2%2B4y=%2B9 Add 9 to both sides


1%28x%2B1%29%5E2-1%2B1y%5E2%2B4y=%2B9 Complete the square for the x terms


1%28x%2B1%29%5E2-1%2B1%28y%2B2%29%5E2-4=%2B9 Complete the square for the y terms


1%28x%2B1%29%5E2%2B1%28y%2B2%29%5E2-5=%2B9 Combine like terms


1%28x%2B1%29%5E2%2B1%28y%2B2%29%5E2=%2B9%2B5 Add 5 to both sides


1%28x%2B1%29%5E2%2B1%28y%2B2%29%5E2=14 Combine like terms



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Notice how the equation is now in the form %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2. This means that this conic section is a circle where (h,k) is the center and r is the radius.
So the circle has these properties:

CENTER: (-1,-2)

Radius: r=sqrt%2814%29