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 = 100/20 = 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.