Question

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

Solution

## Let equation of parabola be $$y^2=4ax.......(1)$$Parabola is 5 cm deepHence, $$OC=5\ cm$$So, x-coordinate of point A=5It can be seen from figure$$AB=20\ cm$$Since parabola is symmetric along x-axis$$AC=\dfrac{1}{2}\times AB=10\ cm$$Hence coordinates of point A is (5,10)Since point A (5,10) lies on the parabola, it will satisfy the equation of the parabola.Putting x=5 and y=10 in (1), we get$$y^2=4ax$$$$10^2=4\times a\times5$$$$100=20a$$$$a=5$$Thus, Focus is $$(a,0)=(5,0)$$Maths

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