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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 deep
Hence, $$OC=5\ cm$$
So, x-coordinate of point A=5
It 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 $$(a,0)=(5,0)$$

1079409_1186230_ans_9bb8c9a1b7d9487391c3e2f0937c1596.png

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