The given equation of parabola is:
[tex]x= \frac{1}{24} y^{2} [/tex]
Part 1) Focus of the Parabola
In order to find the focus and equation of directrix, we first have to convert the given equation to standard form of parabola.
[tex]24x= y^{2} \\ \\
4*6(x)= y^{2} \\ \\
(y-0)^{2} =4*6*(x-0) [/tex]
The focus of the general equation of parabola shown below lies at (h+p, k)
[tex](y-k)^{2}=4p(x-h) [/tex]
Comparing our equation to the general equation we get:
h=0
k=0
p=6
So the focus of given parabola will be (0+6, 0) = (6,0)
Part 2) Directix of the Parabola
The directrix of the general parabola shown above lies at:
x = h - p
Using the values of h and p, we get
x = 0 - 6
x = -6
So, the directrix of the given parabola has the equation x = -6
