Find the center and radius of the circle represented by the equation below.
\[
x^{2}+y^{2}-18 x+10 y+25=0
\]

Answer

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Answer

Square root the constant term to find the radius: \(r = \sqrt{81} \Rightarrow r = 9\)

Steps

Step 1 ：Complete the square for both x and y terms: \((x^2 - 18x) + (y^2 + 10y) = -25\)

Step 2 ：Add square of half of the coefficients of x and y to both sides: \((x^2 - 18x + 81) + (y^2 + 10y +25) = -25 + 81 + 25\)

Step 3 ：Rewrite in standard form and find the center: \((x - 9)^2 + (y + 5)^2 = 81 \Rightarrow Center:\, (9, -5)\)

Step 4 ：Square root the constant term to find the radius: \(r = \sqrt{81} \Rightarrow r = 9\)