Google Classroom
GeoGebraGeoGebra Classroom

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 to 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.