Answers:
Center = (1, 5)
Radius = 3
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Work Shown:
[tex]x^2+y^2-2x-10y+17 = 0\\\\(x^2-2x)+(y^2-10y)+17 = 0\\\\(x^2-2x+0)+(y^2-10y+0)+17 = 0\\\\(x^2-2x+1-1)+(y^2-10y+25-25)+17 = 0\\\\(x^2-2x+1)+(y^2-10y+25)+(-1-25+17) = 0\\\\(x-1)^2+(y-5)^2-9 = 0\\\\(x-1)^2+(y-5)^2 = 9\\\\(x-1)^2+(y-5)^2 = 3^2[/tex]
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Explanation:
The idea is to complete the square for the x and y terms separately.
Notice the jump from step 3 to step 4 has the first 0 turn into 1-1, and the second 0 turn into 25-25. This is to help complete the square for each part.
The x^2-2x+1 factors to (x-1)^2 and y^2-10y+25 factors to (y-5)^2
Once we reach the last step, we have something in the form [tex](x-h)^2+(y-k)^2 = r^2[/tex]
Center = (h,k) = (1,5)
Radius = r = 3
