Questions on Algebra: Quadratic Equation answered by real tutors!

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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.: 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(9862) 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^2-8x+y^2+4y-205=0 Start with the given equation


x^2-8x+y^2+4y=+205 Add 205 to both sides


(x-4)^2-16+y^2+4y=205 Complete the square for the "x" terms. Note: Let me know if you need help completing the square.


(x-4)^2-16+(y+2)^2-4=205 Complete the square for the "y" terms


(x-4)^2+(y+2)^2-20=205 Combine like terms


(x-4)^2+(y+2)^2=205+20 Add 20 to both sides


(x-4)^2+(y+2)^2=225 Combine like terms




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Notice how the equation is now in the form (x-h)^2+(y-k)^2=r^2. 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(225)=15