- #1

PotatoSalad

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I'm hopelessly stuck on this question. Any help will be greatly appreciated.

http://img92.imageshack.us/img92/3983/parabolayp5.jpg

I have managed to show that the gradient of the line PA is (2p/y) and FN is (-y/2p) so those 2 lines are perpendicular. But this is about the only progress I have made with the question.

Thanks for your help.

EDIT:

Sorry, just noticed my diagram is slightly wrong. The point A should be on the y-axis and should also intersect with FN.

*Prove that if we have a parabolic mirror with focus at F and axis of symmetry the x-axis, then a light ray emmited from F will be reflected parallel to the x-axis.*

To prove this consider the parabola y^2=4px (where the focus is at the point (p,0) and the directrix is the line x=-p) and the diagram (below) where N is the point on the directrix which is nearest to P and AP is a tangent to the parabola. Consider the gradients of FN and AP. Use this information to show that the triangle PAF is similar to PAN.To prove this consider the parabola y^2=4px (where the focus is at the point (p,0) and the directrix is the line x=-p) and the diagram (below) where N is the point on the directrix which is nearest to P and AP is a tangent to the parabola. Consider the gradients of FN and AP. Use this information to show that the triangle PAF is similar to PAN.

http://img92.imageshack.us/img92/3983/parabolayp5.jpg

I have managed to show that the gradient of the line PA is (2p/y) and FN is (-y/2p) so those 2 lines are perpendicular. But this is about the only progress I have made with the question.

Thanks for your help.

EDIT:

Sorry, just noticed my diagram is slightly wrong. The point A should be on the y-axis and should also intersect with FN.

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