Question

The focus of a parabolic mirror is at a distance of 6 cm from its vertex. If the mirror is 20 cm deep, find its diameter.

Answer 1

Here O is the vertex and A is the focus of a parabolic mirror.

So,

OA = a = 6 cm

Required equation of the parabola is, y² = 4ax

or y² = 24x

Let OD is the deep of the mirror, OD = 20 cm

BC is the diameter of the mirror and x-coordinate of the points B, C and D is 20

From figure, points, B and C satisfies the equation of the parabola.

Therefore, y² = 24 x 20 = 480

or y = ± 21.9

Coordinate of B is (20, 21.9) and the coordinate of C is (20, -21.9).

Therefore, diameter of the mirror is = (21.9 + 21.9) cm = 43.8 cm