Answer:
1 in
Step-by-step explanation:
We are given that
Diameter of casting=8 in
Radius of casting=[tex]\frac{Diameter}{2}=4 in[/tex]
Depth of casting=4 in
We have to find the distance of light bulb should be from the vertex
It means the reflector passing through the point (4,4).
Equation of parabola along y-axis is given by
[tex]x^2=4ay[/tex]
Using the equation substitute x=4 and y=4
[tex]16=16a[/tex]
[tex]a=\frac{16}{16}=1[/tex]
The focus of parabola is at (0,a).
Therefore, the focus of reflector=(0,1)
Hence, the light bulb should be placed 1 in far from the vertex.
The distance of light bulb can be calculated using equation of parabola. The parabola is a plane curve which is U-shaped.
The distance of light bulb is [tex]1\:\rm in[/tex].
Given:
The diameter is [tex]8\:\rm in[/tex].
The radius is [tex]=\frac{d}{2}=\frac{8}{2}=4 \:\rm in[/tex].
The depth is [tex]4\:\rm in[/tex].
Since the depth is [tex]4\:\rm in[/tex] and radius is [tex]4\:\rm in[/tex] so reflector passes through the point [tex](4,4)[/tex].
Write the equation of parabola for y-axis.
[tex]x^2=4ay[/tex]
Putting [tex]4[/tex] for [tex]x[/tex] and [tex]4[/tex] for [tex]y[/tex].
[tex]4^2=4\times a\times 4\\a=\frac{16}{16}\\a=1[/tex]
The focus of a parabola is [tex](0,1)[/tex].
The distance of light bulb is [tex]1\:\rm in[/tex].
Learn more about parabola here:
https://brainly.com/question/9201543
