If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.


The origin of the coordinate plane is taken at the vertex of the parabolic reflector in such a way that the axis of the reflector is along the positive x – axis.


This can be diagrammatically represented as



The equation of the parabola is of the form y2 = 4ax (as it is opening to the right)


Since, the parabola passes through point A(10, 5), 102 = 4a(5)


100 = 20a


a = = 5


Therefore, the focus of the parabola is (a, 0) = (5,0), which is the mid – point of the diameter.


Hence, the focus of the reflector is at the mid-point of the diameter.


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