Question

A parabola reflector is 15 cm deep and its focus is at a distance of 5 cm from its vertex. Find the diameter of the reflector.

Answer 1

Let the vertex, focus and diameter of parabolic reflecter are (0,0), S(5,0) and AB respectively.
The diameter AB is at a distance of 15 cm from the vertex.
Let the co-ordinates of A=(15,k)
Equation of parabola
`y^(2)=4ax`
Co-ordinates of focus = (a,0) = (5,0)
`rArr" "a=5`
`:." "y^(2)=20x`
`:." "k^(2)=20xx15=300`
`rArr" " k=10sqrt(3)`
Therefore, AB=2k=20sqrt(3)cm`.