SOLUTION: How would I complete the square for both x and y and find the equation of the circle for the given equation x^2-8x+y^2+4y-205=0. I also have the same question for the following equ

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: How would I complete the square for both x and y and find the equation of the circle for the given equation x^2-8x+y^2+4y-205=0. I also have the same question for the following equ      Log On


   

Question 167715: How would I complete the square for both x and y and find the equation of the circle for the given equation x^2-8x+y^2+4y-205=0. I also have the same question for the following equation x^2+12x+y^2-14y-204=0.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first (which hopefully will help you do the second)


# 1




x%5E2-8x%2By%5E2%2B4y-205=0 Start with the given equation


x%5E2-8x%2By%5E2%2B4y=%2B205 Add 205 to both sides


%28x-4%29%5E2-16%2By%5E2%2B4y=205 Complete the square for the "x" terms. Note: Let me know if you need help completing the square.


%28x-4%29%5E2-16%2B%28y%2B2%29%5E2-4=205 Complete the square for the "y" terms


%28x-4%29%5E2%2B%28y%2B2%29%5E2-20=205 Combine like terms


%28x-4%29%5E2%2B%28y%2B2%29%5E2=205%2B20 Add 20 to both sides


%28x-4%29%5E2%2B%28y%2B2%29%5E2=225 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,-2)

Radius: r=sqrt%28225%29=15