An Equation of a Parabola Is Given $$4 x ^ { 2 } + 28 x + 40 y + 209 = 0$$

Multiple Choice

An equation of a parabola is given. Write the equation of the parabola in standard form, and identify the
focus and the equation of the directrix.
- $$4 x ^ { 2 } + 28 x + 40 y + 209 = 0$$

A) $\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = - 10 ( y + 4 )$
focus: $\left( - \frac { 7 } { 2 } , - \frac { 13 } { 2 } \right) ;$ directrix $: y = - \frac { 3 } { 2 }$
B) $( x + 14 ) ^ { 2 } = - 40 \left( y + \frac { 13 } { 40 } \right)$
focus: $\left( - 14 , - \frac { 387 } { 40 } \right) ;$ directrix: $y = - \frac { 413 } { 40 }$
C) $\left( x - \frac { 7 } { 2 } \right) ^ { 2 } = - 10 ( y + 4 )$
focus: $\left( \frac { 7 } { 2 } , - \frac { 13 } { 2 } \right) ;$ directrix: $y = - \frac { 3 } { 2 }$
D) $\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = - 10 ( y - 4 )$
focus: $\left( - \frac { 7 } { 2 } , \frac { 3 } { 2 } \right)$ ; directrix: $y = \frac { 13 } { 2 }$