Write the Equation in Standard Form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$

Write the equation in standard form: $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Then, if possible, identify the center and radius of the circle. If the equation represents a degenerate case, give the solution set.
- $$x ^ { 2 } + y ^ { 2 } - 4 x + 2 y + 5 = 0$$

A) $( x - 2 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 25$ ; Center: $( - 2,1 )$ ; Radius: 5
B) $( x - 2 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 25$ ; Center: $( 2 , - 1 )$ ; Radius: 5
C) $( x - 2 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 0$ ; Degenerate case (single point) : $\{ ( 2 , - 1 ) \}$
D) $( x - 2 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = - 5$ ; Degenerate case: \{ \}