The given equation of the parabola is expressed as
(y + 2)^2 = 12(x - 1)
The first step is to graph the parabola. The graph is shown below
The standard equation of a parabola whose axis is parallel to the x axis is expressed as
(y - k)^2 = 4p(x - h)
where
h and k are the x and y coordiantes of the vertex
focus = (h + p, k)
directrix = x = h - p
By comparing the given equation with this equation, we can see that the axis of the parabola is parallel to the x axis
By comparing the equation with the standard form equation,
B) h = 1, k = - 2
vertex = (1, - 2)
C) 4p = 12
p = 12/4 = 3
focus = (1 + 3, - 2)
focus = (4, - 2)
D) The vertex is halfway between the focus and directrix. Thus, the directrix would be x = - 2
E) The lactus rectum is a line passing through the focus and touching the two ends of the curve. From the graph, endpoints of the lactus rectum are
(4, 5) and (4, - 8)
