Answer
$$\eqalign{
& {\text{Focus: }}\left( {7, - 1} \right) \cr
& {\text{directrix: }}y = - 9 \cr
& {\text{axis of symmetry: }}x = 7 \cr} $$
Work Step by Step
$$\eqalign{
& {\left( {x - 7} \right)^2} = 16\left( {y + 5} \right) \cr
& {\text{This equation is written in the form }}{\left( {x - h} \right)^2} = 4p\left( {y - k} \right){\text{ }} \cr
& {\text{represents Parabola with horizontal axis of symmetry}} \cr
& {\text{of Symmetry and Vertex }}\left( {h,k} \right). \cr
& \underbrace {{{\left( {x - 7} \right)}^2} = 16\left( {y + 5} \right)}_{{{\left( {x - h} \right)}^2} = 4p\left( {y - k} \right){\text{ }}} \cr
& {\text{Let }}k = - 5,\,\,\,\,h = 7 \cr
& 4p = 16 \cr
& p = 4 \cr
& {\text{Focus}}\left( {h,p + k} \right){\text{ and directrix }}y = - p + k \cr
& {\text{Axis of symmetry }}x = h \cr
& {\text{Focus: }}\left( {7,4 - 5} \right) \cr
& {\text{Focus: }}\left( {7, - 1} \right) \cr
& {\text{directrix: }}y = - 4 - 5 \cr
& {\text{directrix: }}y = - 9 \cr
& {\text{axis of symmetry: }}x = 7 \cr
& \cr
& {\text{Focus: }}\left( {7, - 1} \right) \cr
& {\text{directrix: }}y = - 9 \cr
& {\text{axis of symmetry: }}x = 7 \cr} $$
