Answer:
[tex]y=\frac{1}{20}x^2[/tex]
Step-by-step explanation:
In this problem
we have
F(0,5) and directrix at y=-5
so
Is a vertical parabola open upward
we know that
The equation of a vertical parabola in standard form is
[tex](x-h)^2=4p(y-k)[/tex]
where
p is the focal distance
(h,k) is the vertex
we have
The vertex is the origin (0,0)
and
p=5
substitute
[tex](x-0)^2=4(5)(y-0)[/tex]
[tex]x^2=20y[/tex]
[tex]y=\frac{1}{20}x^2[/tex]
