SOLUTION: Please help me with this problem: Find the distance between the focus and vertex of the parabola whose equation is {{{y^2 = 8x}}}.

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Question 1002658: Please help me with this problem:
Find the distance between the focus and vertex of the parabola whose equation is y%5E2+=+8x.
Found 2 solutions by MathLover1, Boreal:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y%5E2+=+8x

variable p is one you'll need because it represents the distance between the vertex and the focus
you have sideways parabola and its equation is:
4p%28x+-h%29+=+%28y-k%29%5E2
from given, we know that h=0 and k=0; so the vertex is at (0,0)
4p%2Ax+=+y%5E2=> compare to y%5E2+=+8x, you see 4p=8=>p=2
then the distance between the vertex and the focus is 2 and the focus is at (2,0)






Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
y^2=8x is a horizontal parabola.
4p(x-h)=(y-k)^2
4p=8,
p=2
focus is 2 units to the right of the vertex, which is (0,0)
graph%28300%2C200%2C-10%2C10%2C-10%2C10%2Csqrt%288x%29%2C-sqrt%288x%29%29