Question

how do you find the focus and directrix in a parabola ? (x+2)^2 = -8(y-1)

Answer 1

the equation for a parabola is x^2=4py, p being the focus. In your equation 4p=-8 so the focus = -2

Answer 2

I found p and I know the directriz should be y= -p but the book gives me different numbers for the directrix and the focus I cant seem to understand how they do it

Answer 3

what does the book say?

Answer 4

according to the book the directrix is y= 3 and the focus is (-2,-1) where did the negative one come from ? and why 3? shouldnt it be 2 since p is negative 2 ?

Answer 5

oh because you have to take into account the shift, since it doesnt start at the origin

Answer 6

i have for vertex (-2,1) which is right in the book but why does it turn to negative at the focus?

Answer 7

the vertex of your equation is (-2,1) so your focus should be 2 below this, (-2,-1)

Answer 8

because your graph is a parabola facing downwards so the focus will be below the vertex

Answer 9

and the directrix will be 2 above the vertex which will be y=3

Answer 10

thanks i get it now :)

Answer 11

np :)