Parabola: Reflective Property and Distance

Each ray starting from

will travel, hit the parabola at some point

and reflect to

. The distance traveled equals the sum of the distance from

and

. Because, by the definition of a parabola,

, we have that the distance traveled is the same as the distance from

to the directrix, no matter where we started. This distance will just be

. This means the 10 rays starting at the different points will all travel the same distance by the time they reach

. If they are moving at the same speed, they will arrive simultaneously. Animate the diagram to see this happen.

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