SOLUTION: Identify The focus and the directrix of the graph of this equation please x = 1/36 * y ^ 2

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Question 1159536: Identify The focus and the directrix of the graph of this equation please
x = 1/36 * y ^ 2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given: x+=+%281%2F36%29y%5E2
If a parabola has a horizontal axis, the standard form of the equation of the parabola is this:
%28y+-+k%29%5E2+=+4p%28x+-+h%29, where p%3C%3E+0
.
The vertex of this parabola is at (h, k).
The focus is at (h+%2B+p, k).
The directrix is the line x+=+h+-+p
rewrite your parabola in vertex form:
%281%2F36%29+y+%5E+2=x
y+%5E+2=x%2F%281%2F36%29
%28y-0%29+%5E+2=36%28x-0%29
compare to
%28y+-+k%29%5E2+=+4p%28x+-+h%29
=> h=0 and +k=0 ->vertex is at (0,+0)
4p=36->p=36%2F4->p=9
The focus is at (h+%2B+p, k)=>(0+%2B+9, 0)=>(9, 0)
directrix is x+=+h+-+p=>x+=+0+-+9=>x+=+-9