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If a parabolic reflector is 20 cm in dia...

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

Text Solution

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Let the vertex of parabolic is AB.
Diameter AB is at a distance 5 cm from vertex O.
`:." "OM=5`
and `AM=(1)/(2)AB=-(1)/(2)xx20=10`
Therefore, coordinates of point A
`-=(5,10)`
From the equation of parabola
`y^(2)=4ax`
`(10)^(2)=4a(5)`
`rArr" "a=5`
Now, coordinates of focus `-=(a,0)-=(5,0)`
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