Answer:
[tex]p=1/2\ or\ 0.5\ inches[/tex]
Step-by-step explanation:
From the question we are told that
Equation of cross section is [tex]y+5= \frac{1}{2x^2}[/tex]
Generally the equation can be rewritten mathematically as
[tex]y+5= \frac{1}{2}x^2[/tex]
[tex]x^2=(y+5)2[/tex]
[tex](x-0)^2=(y-(-5))2[/tex]
Generally the equation of a parabola with vertical axis is mathematically given by
[tex](x - h)2 = 4p(y - k)[/tex]
Therefore comparing equations
[tex](x-0)^2=(y-(-5))2[/tex]
[tex]4p=2[/tex]
[tex]p=2/4[/tex]
The distance from the bulb to the vertex of the cross section is given by
[tex]p=1/2\ or\ 0.5\ inches[/tex]
