Precalculus question involving a laser reflecting inside a parabola. Will give medals and follow!

Question

anonymous · Answer

attachment

anonymous · Answer

So far I know from part B that the equation of the parabola is x^2 = -(8/3)*(y - 6).

anonymous · Answer

I also know that I can find the height of point R using trigonometry in terms of the x,y coordinates of points P and Q. What I do not know is whether there is a way to find the relevant angle explicitly, without using calculus.

anonymous · Answer

@ganeshie8 This problem was a bit confusing, and I thought you might have some insight. I will post part a below for completeness.

anonymous · Answer

Part A) The   span   of   the   parabolic   arch   in   figure   B   is   8   m.   At   a   distance   of   2   m   from   the   center,   the   vertical   clearance   is   4.5   m.   Find   the   height   of   the   arch.   Hint:   Choose   a   convenient   coordinate   system   in   which   the   equation   of   the   parabola   will   have   the   form   x^2   =   -4p(y-k)

anonymous · Answer

Figure B is posted below.

anonymous · Answer

http://en.wikipedia.org/wiki/Parabolic_reflector Look here to see how all the rays are reflected to the focus: http://en.wikipedia.org/wiki/Parabolic_reflector#mediaviewer/File:Parabola_with_focus_and_arbitrary_line.svg So just find the focus =)

anonymous · Answer

Thanks, Pitamar! Your above link was very helpful! The focus would be (0, 16/3), so the height of point R will be 16/3. :D