Question

What is the equation of a parabola with (-1,-3) as its focus and y=1 as its directrix?

Answer 1

Hmm, y=1 is directix
means it opens up or down
we will be using
(x-h)²=4p(y-k) where (h,k) is vertex and p is the distnace from focus to vertex and from vertex to direcitx
focus is (-1,-3)
find distance between y values because directix is a y value
midpoint is the vertex
from -3 to 1 is 2 units
since focus is below directix, it opens down, and p is negative
it is 2 units above focus
so at (-1,-1)
and p=-2

(x-(-1))²=4(-2)(y-(-1))
(x+1)²=-8(y+1) is da equation