An Equation of a Parabola Is Given $$16 y ^ { 2 } - 104 y + 288 x + 1,033 = 0$$

An equation of a parabola is given. Write the equation of the parabola in standard form, and identify the
vertex and the focus.
- $$16 y ^ { 2 } - 104 y + 288 x + 1,033 = 0$$

A) $\left( y - \frac { 13 } { 4 } \right) ^ { 2 } = - 18 ( x - 3 )$
vertex: $\left( 3 , \frac { 13 } { 4 } \right)$ ; focus $\left( - \frac { 15 } { 2 } , \frac { 13 } { 4 } \right)$
B) $\left( y - \frac { 13 } { 4 } \right) ^ { 2 } = - 18 ( x + 3 )$
vertex: $\left( - 3 , \frac { 13 } { 4 } \right)$ ; focus $\left( - \frac { 15 } { 2 } , \frac { 13 } { 4 } \right)$
C) $\left( x + \frac { 13 } { 4 } \right) ^ { 2 } = - 18 ( y + 3 )$
vertex: $\left( - \frac { 13 } { 4 } , - 3 \right)$ ; focus $\left( - \frac { 13 } { 4 } , - \frac { 15 } { 2 } \right)$
D) $\left( x - \frac { 13 } { 4 } \right) ^ { 2 } = - 18 ( y + 3 )$
vertex: $\left( \frac { 13 } { 4 } , - 3 \right) ;$ focus $\left( \frac { 13 } { 4 } , - \frac { 15 } { 2 } \right)$