Question

The equation of the parabola whose focus is at (0, 5) and directrix at y = -5 is:

Answer 1

Answer:

$y=\frac{1}{20}x^2$

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

$(x-h)^2=4p(y-k)$

where

p is the focal distance

(h,k) is the vertex

we have

The vertex is the origin (0,0)

and

p=5

substitute

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

$x^2=20y$

$y=\frac{1}{20}x^2$