What is the focus,directrix, axis and vertex of the equation x-2=1/8 (y+1)^2. Graph too if possible

Expert Answers
baxthum8 eNotes educator| Certified Educator

`x - 2 = (1/8)(y+1)^2`

Parabola opening towards right as x is positive and y is squared.

Vertex = (2, -1) from general (graphing) form of a parabola

Which means axis is horizontal:  y = -1

Multiply both sides by 8 to isolate `(y+1)^2`

you get  `8(x - 2) = (y + 1)^2`

this means 4p = 8, (from `(x-h)^2 = 4p(y - k))`

therefore p = 2 which means focus is 2 units to right of vertex,

focus:  (4, -1)and directrix is vertical line passing through point 2 units to left of vertex

directrix:  x = 0

(sorry, can't seem to get graph for x= on this system, hopefully you can follow from information to determine a graph now that you know which way it opens and vertex)