What is the equation of the parabola with a focus at (0, -5) and directrix y = 5? my answer was x=-1/20y^2

We are given focus at (0, -5) and directrix y = 5.

The formula for equation of directrix is y = k - p.

And formula for focus is  (h, k + p).

On comparing focus  (0, -5) and  (h, k + p), h=0.

k+p = -5   ----------------equation(1)

On comparing directrix y = k - p and y = 5.

k- p = 5    ----------------equation(2)

Adding eqautions (1) and (2).

 k+p = -5

 k- p = 5

_________

2k = 0.

k=0

Plugging k=0 in first equation, we get

k+p = -5

0 + p = -5.

p = -5.

We know, parabola equation (x - h)^2 = 4p (y - k)

Plugging h,k and p value in the above equation, we get

(x - 0)^2 = 4(-5) (y - 0)

x^2  = -20y.

Dividing both sides by -20, we get

-1/20 x^2 = y.

Or

the correct answer is the second option

is means division by fractions

step-by-step explanation: