The focus of a parabolic mirror is at a distance of 5 cm from its vertex. If the mirror is 45 cm deep, find the distance AB

Explanation

From the given figure, we have equation of the parabolic mirror is

y2 = 4ax ……………..(1)

Given:

OF =5, F be the focus of (1)

Since `F = (a, 0) = (5,0) ∴ a = 5`

And `OC = 45 = Depth of the mirror. A = (45,y)`

and `B = (45,-y) We have, x = 45, y = y and a = 5`
then equation (1) gives, `y1 =4 x 5 x 45 = 900 y = ± 30 AB = 2y = 2 x 30 = 60 cm`