Question

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

Answer 1

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 (5, 10),

$10^2 = 4a(5)$
$⇒ 100 = 20a$
$⇒ a = \frac{100}{20} = 5$

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.