Answer:
Explanation:
Given:
[tex]x=-\frac{1}{8}y^2[/tex]
The distance between the vertex and the focus is called a focal length or p. To find it, we must use the standard equation for the given parabola which is right-left facing with a vertex at (h,k) and a focal length |p|.
[tex]4p(x-h)=(y-k)^2[/tex]
So, we simplify the given equation:
[tex]\begin{gathered} x=-\frac{1}{8}y^2 \\ \text{Simplify and rearrange} \\ -8x=y^2 \\ \text{Next, we factor:} \\ 4(-2)x=y^2 \\ We\text{ rewrite this as} \\ 4(-2)(x-0)=(y-0)^2 \end{gathered}[/tex]
Therefore, the value of p or focal length is 2 since we use the absolute value or positive value.
