Answer: Center = (-1, 10)
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Step-by-step explanation:
If we had x^2+2x + ___, then 1 must go in the blank so that we have x^2+2x+1 = (x+1)^2
So we must add 1 to both sides to complete the square for the x terms. To find this value '1' we take half of the x coefficient 2 to get 1, then square it to get 1^2 = 1.
We have
x^2+y^2 + 2x - 20y - 20 = 0
x^2+y^2 + 2x - 20y - 20 + 1 = 0 + 1
(x^2+2x+1) + y^2 - 20y - 20 = 1
(x^2+2x+1) + y^2 - 20y = 1 + 20
(x+1)^2 + y^2 - 20y = 21
After completing the square for the x terms. Repeat for the y terms. Take half of -20 to get -10, which squares to 100. Add this to both sides
(x+1)^2 + y^2 - 20y = 21
(x+1)^2 + y^2 - 20y + 100 = 21+100
(x+1)^2 + (y - 10)^2 = 121
The equation is in the form (x-h)^2 + (y-k)^2 = r^2 where
The center is (h, k) = (-1, 10). The radius is r = 11.