Equation of Parabola is:
\(y = \frac{1}{4p} (x-h)^2 + k\)
where (h,k) is vertex and p = k - directrix
The vertex can be found by taking midpoint between focus and directrix:
Notice we will use y-coordinate since directrix is horizontal line (y=?)
\(mid = \frac{(-6) +2}{2} = -2\)
This is the y-value of vertex or k. The x-value of vertex is same as focus.
\((h,k) = (4,-2)\)
Next find p:
\(p = k - d = -2 - 2 = -4\)
Finally we can write equation of parabola by plugging in values for h,k,p:
\(y = \frac{1}{4(-4)}(x-4)^2 -2 = - \frac{1}{16}(x-4)^2 -2\)
