# Parabolic Headlight where should bulb be located Locus and Conic unit

• aisha
In summary, the link provided is a diagram of a cross section of a parabolic reflector for a headlight. The question is to determine where the bulb should be located if it is positioned at the focus. The equation for this parabola is y^2 = 4px, where p is the focus. The point (8,16) on the parabola is where the light bulb should be placed, as all lines to the parabola reflect parallel to the x-axis at that point. This is an application question for locus and conics, and the parabolic nature of the reflector is evident from the given information.
aisha
http://ca.pg.photos.yahoo.com/ph/sikandar1984/detail?.dir=9181&.dnm=8e2e.jpg&.src=ph

This link is a diagram for this question

It says the cross section of a parabolic reflector of a headlight is shown in the diagram. Determine where the bulb should be located if it is positioned at the focus?

Um what is the cross section? The x and y axis? Where they meet?

Do I have to find an equation? Or coordinate? Or do I just describe where it should be?

This is an application question for locus and conics I think this is an application with a parabola conic but not too sure. I have an equation for the bulb but its probably wrong, it is

$$x^2= \frac {1} {32} y^2$$

this is the equation of a parabola conic opening towards the right like the diagram. Please help me out! Thanks

Last edited by a moderator:
aisha said:
$$x^2= \frac {1} {32} y^2$$

this is the equation of a parabola conic opening towards the right like the diagram. Please help me out! Thanks
The equation for this parabola is:

$$y^2 = 4px$$ where p is the focus

So if the point (8,16) is on the parabola, what is p?

That is where you would put the light bulb. At that point all lines to the parabola reflect parallel to the x-axis - which makes it a beam of light.

[Note: the parabola is obviously not drawn to the proper scale.]

AM

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where did u get the point (8,16) is this parabola opening towards the right like the diagram?

aisha said:
where did u get the point (8,16) is this parabola opening towards the right like the diagram?

Your picture shows that at 8 units from the vertex, the "width" of the parabola is 32: If your coordinate system is set up so that (0,0) is at the vertex then 1/2 of that 32 is positive, 1/2 negative. Choosing positive x to the right, positive y upward, that corresponds to x= 8, y= 32/2= 16 or y= -32/2= -16.

aisha said:
This is an application question for locus and conics I think this is an application with a parabola conic but not too sure.

aisha, Don't you believe what YOU write? The problem SAYS "a parabolic reflector". Why would you be "not too sure" it really IS a parabola?

the light bulb will be at point 8,0

8 being the focus when i subbed a point into the equation

## 1. What is a parabolic headlight?

A parabolic headlight is a type of headlight that uses a parabolic reflector to focus the light from a bulb into a beam, allowing for better visibility on the road.

## 2. Where should the bulb be located in a parabolic headlight?

The bulb should be located at the focal point of the parabolic reflector, which is typically at the center of the reflector. This ensures that the light is reflected and focused correctly.

## 3. What is the locus in relation to a parabolic headlight?

The locus refers to the path of light that is reflected by the parabolic reflector. In a parabolic headlight, the locus of the reflected light is a parabola.

## 4. How does the conic unit affect a parabolic headlight?

The conic unit represents the shape of the parabolic reflector. A higher conic unit, such as a 2.0, means that the reflector is more curved and will produce a tighter, more focused beam of light. A lower conic unit, such as a 1.5, will produce a wider beam of light.

While parabolic headlights are commonly used in vehicles, they are not necessarily the most efficient type of headlight. LED headlights, for example, are known to be more energy-efficient and have a longer lifespan compared to traditional halogen headlights used in parabolic headlight systems.

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