SOLUTION: State the center and the radius of the circle given X^2-10X+y^2-8y=8. I dont even know how to solve this.

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Question 204734: State the center and the radius of the circle given X^2-10X+y^2-8y=8.
I dont even know how to solve this.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Start with te general form of the equation of a circle with center at (h, k) and radius r.
%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2
The given equation is:
x%5E2-10x%2By%5E2-8y+=+8 First, group the terms as shown:
%28x%5E2-10x%29%2B%28y%5E2-8y%29+=+8 Now you need to "complete the squares" in both the x-terms and the y-terms. You do this by adding the square of half the x-coefficient and the square of half the y=coefficient to both sides of the equation.
The square of half the x-coefficient is: %28-10%2F2%29%5E2+=+25 and the square of half the y-coefficient is: %28-8%2F2%29%5E2+=+16 so...
%28x%5E2-10%2B25%29%2B%28y%5E2-8y%2B16%29+=+8%2B25%2B16 On the left side, factor the x-group and factor the y-group.
%28x-5%29%5E2%2B%28y-4%29%5E2+=+29 Now compare this with the general form from above:
%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2
You can see that:
h+=+5, k+=+4%29, and r%5E2+=+49
So the center (h, k) is at (5, 4) and the radius, r+=+sqrt%2849%29 or r+=+7