Equation of Parabola is:
[tex]y = \frac{1}{4p} (x-h)^2 + k [/tex]
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=?)
[tex]mid = \frac{(-6) +2}{2} = -2 [/tex]
This is the y-value of vertex or k. The x-value of vertex is same as focus.
[tex](h,k) = (4,-2)[/tex]
Next find p:
[tex]p = k - d = -2 - 2 = -4[/tex]
Finally we can write equation of parabola by plugging in values for h,k,p:
[tex]y = \frac{1}{4(-4)}(x-4)^2 -2 = - \frac{1}{16}(x-4)^2 -2 [/tex]
