Question

HELP!!! Write the equation of a parabola with focus (-2,4) and directrix y=2 . Show your work

Answer 1

K, so since directix is below focus, it opens up (2<4)
and directix is y=something so equation is (x-h)^2+4p(y-k) where (h,k) is vertex and p is distance from focus to vertex. if it opens down, p<0, if it opens up, p>0
and the vertex is in the middle of the focus and directix

so

distance bewten (-2,4) and y=2 is 2 units
2/2=1, so 1 unit down from focus
vertex is in the middle so it is at (-2,3)
also, opens up so p=1

vertex (-2,3)
p=1
(x-(-2))^2=4(1)(y-3)
(x+2)^2=4(y-3) is an equation