ANSWER
[tex]p = - 2[/tex]
EXPLANATION
The given equation is
[tex]x = - \frac{1}{8}{y}^{2} [/tex]
Multiply both sides by -8
[tex] \implies \: {y}^{2} = - 8x[/tex]
We now compare this to the general equation of the parabola:
[tex] {y}^{2} = 4px[/tex]
This implies that,
[tex]4p = - 8[/tex]
Divide both sides by 4.
[tex]p = \frac{ - 8}{4} [/tex]
[tex]p = - 2[/tex]
