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: \(r = \sqrt{81} \Rightarrow r = 9\)