Write the Equation of the Hyperbola in Standard Form $$4 y ^ { 2 } - 16 x ^ { 2 } + 40 y - 32 x + 20 = 0$$

Multiple Choice

Write the equation of the hyperbola in standard form. Identify the center and vertices.
- $$4 y ^ { 2 } - 16 x ^ { 2 } + 40 y - 32 x + 20 = 0$$

A) $\frac { ( y - 5 ) ^ { 2 } } { 16 } - \frac { ( x - 1 ) ^ { 2 } } { 4 } = 1$
center: $( - 1 , - 5 )$ ; vertices: $( - 1 , - 9 ) , ( - 1 , - 1 )$
B) $\frac { ( y + 5 ) ^ { 2 } } { 16 } - \frac { ( x + 1 ) ^ { 2 } } { 4 } = 1$
center: $( - 1 , - 5 )$ ; vertices: $( - 1 , - 9 ) , ( - 1 , - 1 )$
C) $\frac { ( y + 5 ) ^ { 2 } } { 16 } - \frac { ( x + 1 ) ^ { 2 } } { 4 } = 1$
center: $( 1,5 )$ ; vertices: $( 1,1 ) , ( 1,9 )$
D) $\frac { ( y - 5 ) ^ { 2 } } { 16 } - \frac { ( x - 1 ) ^ { 2 } } { 4 } = 1$
center: $( 1,5 )$ ; vertices: $( 1,1 ) , ( 1,9 )$