6. Find the center of a circle with the following equation
\[
x^{2}+y^{2}-2 x-12 y-11=0
\]
Center:

Answer

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Answer

The center of the circle is \( \boxed{(1, 6)} \)

Steps

Step 1 ：Rewrite the given equation by completing the square for both x and y terms: \( (x^2 - 2x + 1) + (y^2 - 12y + 36) = 11 + 1 + 36 \)

Step 2 ：Simplify the equation: \( (x - 1)^2 + (y - 6)^2 = 48 \)

Step 3 ：The center of the circle is \( \boxed{(1, 6)} \)