Answer:
centre = (9, - 5 ) and radius = 9
Explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
given
x² + y² - 18x + 10y + 25 = 0
subtract 25 from both sides and collect x / y terms together
x² - 18x + y² + 10y = - 25
using the method of completing the square
add ( add half the coefficient of the x/ y terms )² to both sides
x² + 2(- 9)x + 81 + y² + 2(5)y + 25 = - 25 + 81 + 25
(x - 9)² + (y + 5)² = 81 = 9²
then
centre = (9, - 5 ) and radius = 9