Question

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

Answer 1

Let LOM be the parabolic reflector such that LM is the diameter and ON is its depth.

It is given that ON = 5 cm and LM = 20 cm.

∴ LN = 10 cm

Taking O as the origin, ON along X-axis and a line through O ⊥ ON as Y-axis.

Let the equation of the reflector be

y² = 4ax  ...(i)

The point L has the co-ordinates (5, 10) and lies on parabola given by (i).

Substituting x = 5 and y = 10 in (i), we get

10² = 4a (5)

∴ 100 = 20a

∴ a = 5

Focus is at (a, 0), i.e., (5, 0).