ANSWER
[tex]y = \frac{1}{20} {x}^{2} [/tex]
EXPLANATION
We want to find the equation of the parabola with a focus at (5, 0)
and a directrix at x = -5.
The distance from the focus to the vertex is the same as the distance from the vertex to the directrix.
This implies that the parabola has its vertex at the origin. This distance is
[tex]p = 5[/tex]
This parabola has equation of the form
[tex] {x}^{2} = 4py[/tex]
We plug in p= 5 to get
[tex] {x}^{2} = 4 \times 5y[/tex]
[tex] {x}^{2} = 20y[/tex]
Or
[tex]y = \frac{1}{20} {x}^{2} [/tex]
