Find the coordinates of the centre C and the length of the diameter of a circle with the equation (x-2)^2 + (y+5)^2 = 25

Equation of a circle  ->  (x-a)² + (y-b)^2 = r²     where the centre = (a,b) and the radius = r

Thus using the equation above we can conclude that the centre is (2,-5)

In order to find the diamerer fo the circle, the radius is needed. 

√r² = √25   therefore r = 5    as 2r = diameter = 10

Centre of the circle is (2,-5) and has a diameter of 10