Answer: [tex]x^{2} = 20y[/tex]
Step-by-step explanation:
The directrix given is vertical , so we will use the formula :
[tex](x-h)^{2}=4p(y-k)[/tex]
P is the distance between the focus , that is 5 - 0 = 5
Therefore : p = 5
(h,k) is the mid point between the focus and the directrix , that is
(h,k) = [tex](\frac{x_{1}+x_{2} }{2},\frac{y_{2}+y_{1}}{2})[/tex] = [tex](\frac{0+0}{2} , \frac{5-5}{2})[/tex] = [tex](0,0)[/tex]
Therefore:
h =0
k = 0
substituting into the formula : we have
[tex](x-h)^{2}=4p(y-k)[/tex]
[tex](x-0)^{2}[/tex] = 4(5)([tex]y-0)[/tex]
[tex]x^{2} = 20y[/tex]
Therefore : the equation in vertex form is [tex]x^{2} = 20y[/tex]
