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

Answer

Expert–verified

Hide Steps

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: $(x^{2} - 18 x) + (y^{2} + 10 y) = - 25$

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

Step 3 ：Rewrite in standard form and find the center: $(x - 9)^{2} + (y + 5)^{2} = 81 \Rightarrow C e n t e r : (9, - 5)$

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