1.

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»

Solution :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`.


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