Write an equation of the circle with center \( (5,-3) \) and diameter 8.

To write the equation of a circle, we can use the standard form of the equation of a circle, which is given by: \[ (x - h)^2 + (y - k)^2 = r^2 \] where \((h, k)\) is the center of the circle and \(r\) is the radius. Given the center of the circle \((5, -3)\) and a diameter of 8, we first need to find the radius. The radius \(r\) is half of the diameter: \[ r = \frac{8}{2} = 4 \] Now we can substitute the center \((h, k) = (5, -3)\) and the radius \(r = 4\) into the equation: \[ (x - 5)^2 + (y + 3)^2 = 4^2 \] Calculating \(4^2\): \[ 4^2 = 16 \] Thus, the equation of the circle is: \[ (x - 5)^2 + (y + 3)^2 = 16 \] This is the equation of the circle with center \((5, -3)\) and diameter 8.