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Misc 1 - If parabolic reflector is 20 cm in diameter, 5 cm deep - Miscellaneous

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  1. Chapter 11 Class 11 Conic Sections
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Misc 1 If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus. Let equation of parabola be y2 = 4ax Here we need to find a (focus) Hence, Taking Point A and finding its coordinates 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 = ﷐1﷮2﷯ × 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) y2 = 4ax 102 = 4 ×𝑎 × 5 100 = 20a ﷐100﷮20﷯ = a 5 = a a = 5 Thus, Focus is (a , 0) = (5 , 0)

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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