## anonymous one year ago What is the equation of a parabola with a vertex at (1, -1) and a directrix y = 4.

1. anonymous

@muscrat123

2. anonymous

yes

3. anonymous

and i do not know this

4. anonymous

>.>

5. freckles

hello.

6. freckles

$(x-h)^2=4p(y-k) \\ \text{ where the vertex is } (h,k)$

7. freckles

p's sign is based on whether the vertex is above the directrix or below the directrix if the vertex is above the directrix, then p is positive. if the vertex is below the directrix, then p is negative.

8. freckles

now the other thing p has going for it .. is that it is the distance from the vertex to the directrix (or you can say the distance from the vertex to the focus)

9. freckles

so p tells us two things not just one

10. freckles

it helps to draw what we are given sometimes... |dw:1439673047228:dw| so the directrix is above the vertex so p is negative can you tell me how far the directrix is from the vertex

11. anonymous

thx so much, i think the answer is $y+1= -\frac{ 1 }{ 20 }\left( x-1 \right)^{2}$