Conic sections directrix and focus I do not understand the following:
The equation of a particular parabola is:
$$(y−​23)​​ = -\dfrac{1}{​16}\!\!\!\!\!​​​​(x+3)​^2​​$$
Given the equation of a parabola is - $(y−y_1)​= a(x−x​_1\!\!)^{​2}$​​ - the number in the denominator of a (i.e. $-\dfrac{1}{16}$) is twice the distance between the directrix to the focus. 

Equation of a standard downward facing parabola is $(x-x_1)^2=-4a(y-y_1),$ and in that parabola the perpendicular distance from the focus to the directrix is $2a$,
In your case, $(x_1,y_1)=(-3,23)$ and $4a=16$ which is double of $2a=8.$
