Answer: Our require equation of parabola is given by
[tex]x^2=20y[/tex]
Step-by-step explanation:
Since we have given that
Focus (0,5) -------------(1)
And we know that the general form of focus is given by
Focus (h,k+p) -------------------(2)
So, Comparing both the equations we get that
h = 0
and k+p = 5 ----------------------(3)
And directrix is given by
y = -5
The general form of directrix is given by
y = k-p
Putting the value of y in the above equation :
-5=k-p
p-k=5 ----------------------------(4)
Using (3) and (4), we get that
[tex]p-k=k+p\\\\0=2k\\\\k=0[/tex]
So, putting the value of k in equation (3), we get that
[tex]p=5[/tex]
So, the equation of parabola becomes,
[tex](x-h)^2=4p(y-k)\\\\x^2=4\times 5y\\\\x^2=20y[/tex]
Hence, our require equation of parabola is given by
[tex]x^2=20y[/tex]