We have to find the equation of a circle with center (5,-2) and radius 16.

The equation of a circle with center (h,k) and radius r is given by (x - h)^2 + (y - k)^2 = r^2

Replacing the values for the center and the radius given here we get :

(x - 5)^2 + (y- (-2))^2 = 16^2

=> (x - 5)^2 + (y + 2)^2 = 16^2

=> x^2 + 25 -10x + y^2 + 4 + 4y = 256

=> x^2 + y^2 - 10x + 4y - 227 = 0

**The equation of a circle with center (5,-2) and radius 16 is x^2 + y^2 - 10x + 4y - 227 = 0**

The equation of the circle is:

(x - h)^2 + (y - k)^2 = r^2

The coordinates h and k represent the coordinates of the center of the circle.

We'll substitute the x and y coordinates of the center in the equation of the circle:

(x - 5)^2 + (y + 2)^2 = 16^2

(x - 5)^2 + (y + 2)^2 = 256

**The equation of the circle whose center is C(5 , -2) and radius , r = 16, is:**

**(x - 5)^2 + (y + 2)^2 = 256**