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I cannot figure out how to solve and graph this problem. You are desiginnig a parabolic dish to use for cooking on a camping trip. You plan to make the dish 60cm wide and 30cm deep. Where should you locate the cooking grill so that all of the light that enters the parabolic dish will be reflected toward the food? How does this point relate to the definiton of a parabola? 

Guest Apr 8, 2018
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 #1
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We can orient the dish so that the vertex  is at the origin and the parabola opens upward...

If the dish  is  60cm wide  and 30cm deep, the points  (-30, 30)  and  (30, 30)  are on the graph

 

So......the form we have when the vertex  is  at the origin is this :

 

4py =  x^2    where p  is the distance between the origin and the focal point

 

And since   (30,30)  is on the graph, we have

 

4p (30)  = 30^2

120p = 900        divide both sides by 120

p = 900/120

p = 15/2

 

So.....the cooking grill should be located  at  (0, 0 + p)  =   (0, 15/2)

 

This fits the definition of the parabola because any light waves striking the interior of the dish will be reflected towards the focal point.

 

The function is

 

4 (15/2)y  =   x^2 ⇒  30y  =  x^2  ⇒   y  =  (1/30)x^2

 

 

Here  is the graph   with the focal point  :

 

https://www.desmos.com/calculator/r3x9j7epfp

 

 

cool cool cool

CPhill  Apr 9, 2018
 #2
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Thank you 

Guest Apr 10, 2018

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