Parabolic Headlight where should bulb be located Locus and Conic unit

[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

 

[Andrew Mason]

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

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

 

[aisha]

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

 

[HallsofIvy]

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.

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?

 

[aisha]

the light bulb will be at point 8,0

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