What are the focus and the directrix of the graph of x=1/24 y^2

The given equation of parabola is:



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.



The focus of the general equation of parabola shown below lies at (h+p, k)


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