SOLUTION: Tutors can you help me?* find the center and the radius of the circle given by x^2+8x+y^2+6y-24=0

Algebra ->  Linear-equations -> SOLUTION: Tutors can you help me?* find the center and the radius of the circle given by x^2+8x+y^2+6y-24=0      Log On


   

Question 140867: Tutors can you help me?*
find the center and the radius of the circle given by x^2+8x+y^2+6y-24=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B8x%2By%5E2%2B6y-24=0 Start with the given equation


x%5E2%2B8x%2By%5E2%2B6y=%2B24 Add 24 to both sides


%28x%2B4%29%5E2-16%2By%5E2%2B6y=%2B24 Complete the square for the x terms


%28x%2B4%29%5E2-16%2B%28y%2B3%29%5E2-9=%2B24 Complete the square for the y terms


%28x%2B4%29%5E2%2B%28y%2B3%29%5E2-25=%2B24 Combine like terms


%28x%2B4%29%5E2%2B%28y%2B3%29%5E2=%2B24%2B25 Add 25 to both sides


%28x%2B4%29%5E2%2B%28y%2B3%29%5E2=49 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: (-4,-3)

Radius: r=sqrt%2849%29=7