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

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#### Solution

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 *y*^{2} = 4*ax* (as it is opening to the right).

Since the parabola passes through point A (10, 5), 10^{2} = 4*a*(5)

⇒ 100 = 20*a*

`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.

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