MATH HELP?!
GRADUATION OF 10TH GRADE ON THE LINE!

#1 A car’s headlight contains a parabolic reflector. A special bulb with two filaments is used to produce the high and low beams. The filament placed at the focus produces the high beam and the filament placed off-focus produces the low beam. The equation of the reflector is y=1/12 x^2. How far from the vertex should the filament for the high beam be placed? The x and y values are in centimeters.

#2 Concentric circles have the same center but different radii. Write equations for two concentric circles centered at ( -3, 5) with radii of 7 and 9.

Question

MATH HELP?! 
GRADUATION OF 10TH GRADE ON THE LINE!

#1 A car’s headlight contains a parabolic reflector.  A special bulb with two filaments is used to produce the high and low beams.  The filament placed at the focus produces the high beam and the filament placed off-focus produces the low beam.   The equation of the reflector is   y=1/12 x^2.     How far from the vertex should the filament for the high beam be placed?  The x and y  values are in centimeters.

#2 Concentric circles have the same center but different radii.  Write equations for two concentric circles centered at ( -3, 5) with radii of  7 and 9.

mathmale · Answer

First:  I believe you can completely ignore all the info about the low beam filament:

A car’s headlight contains a parabolic reflector.  
A special bulb with two filaments is used to produce the high and low beams.  
The filament placed at the focus produces the high beam.   
The equation of the reflector is   y=1/12 x^2.     
How far from the vertex should the filament for the high beam be placed?  The x and y  values are in centimeters.

Hint:  The appropriate equation of a parabola that relates to the distance between the focus and the vertex is 

$$4py=x^2$$ Compare this equation to your $$y=\frac{ 1 }{ 12 }x^2$$  and determine the value of p.

this value of p is the answer to, "How far from the vertex should the filament for the high beam be placed?"

anonymous · Answer

No it isnt an exam sir, it is homework help.

mathmale · Answer

@kitties33:  In no way did I mean to imply that you were asking for help with a test question.  don't worry about that!

anonymous · Answer

No there was another person who had posted :b Okay I still dont get it though :/

mathmale · Answer

Rewrite y = (1/12)x^2 as 12y=x^2.

mathmale · Answer

Now please compare this 12y=x^2 to
                                         4py=x^2

and solve for p.

mathmale · Answer

attachment

anonymous · Answer

I am feeling extremely dumb because how do you compare it? is p=12 or does it = 3

anonymous · Answer

I think it is 3 because you multiply it to the 4 for the 12 correct?

mathmale · Answer

12y=x^2=4py, 
so,
12y =4py                     (divide both sides by y)

4p = 12

p = 12/4 = 3.  YES!

mathmale · Answer

So:  how far should we place the high beam filament from the vertex of this parabolic reflector?

anonymous · Answer

3 centimeters? o.O

mathmale · Answer

Perfect.  Nice work!!

anonymous · Answer

Thank you !!!

mathmale · Answer

Hope to work with you again.  For now:  I have to get off the Internet!

anonymous · Answer

Alright thank you for the help :)