Question

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

Answer 1

The diameter of the parabolic reflector, AOB,

AB = 20 cm

and AM = 10 cm

deep of reflector, OM = 5 cm

If OX, OY are the coordinate axis then the point lies on the parabola.

Let the equation of parabola be, y² = 4ax

∴ 10² = 4a × 5

= 100 = 20a

a = `100/20`

∴ a = 5

The focus of the parabola is (a, 0) or (5, 0).