Help with Parabola Question by Monday

[PotatoSalad]

Can somebody please help me with this question. I keep thinking I have made some progress on it and it turns out to be totally useless work. Spent almost 2 days struggling over this problem and 2 others and they have to be done for Monday. I have scanned in the question below.

http://img168.imageshack.us/img168/241/prob6ud2.jpg

If anyone can help me with this it will be greatly greatly appreciated.

 

[abode_x]

considering the gradients of the lines means their slopes. that is, using the slopes show that FN is at right angles with PA.

then you can use a property of a parobala that will let you conclude that triangle PAF is the same as triangle PAN. and so are the corresponding angles.

then you must relate this conclusion to the actual path the ray of light takes when it bounces off the parabola. that is, consider the law of reflection for the flat mirror AP.

 

[PotatoSalad]

considering the gradients of the lines means their slopes. that is, using the slopes show that FN is at right angles with PA.

then you can use a property of a parobala that will let you conclude that triangle PAF is the same as triangle PAN. and so are the corresponding angles.

then you must relate this conclusion to the actual path the ray of light takes when it bounces off the parabola. that is, consider the law of reflection for the flat mirror AP.

Ok thanks adobe. I have managed to prove that the line FN and PA are perpendicular.

What is the property of the parabola that you mention in the 2nd paragraph? I have barely done any work on this type of stuff in the past so I am not sure about it. Is it that the line FP is always the same length as PN? Or is that not true?

Thanks again.

 

[abode_x]

"Is it that the line FP is always the same length as PN? Or is that not true?"

i think that's it. (look at definition of a parabola)

 

[PotatoSalad]

Ok I've got it, it just clicked in my brain this morning. Thanks a lot adobe.