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Example 17 - The focus of a parabolic mirror is at a distance - Parabola - Arch/mirror problem

Example 17 - Chapter 11 Class 11 Conic Sections - Part 2

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Example 17 The focus of a parabolic mirror as shown in Fig 11.33 is at a distance of 5 cm from its vertex. If the mirror is 45 cm deep, find the distance AB (Fig 11.33). Since axis of parabola is in positive x-axis, Equation of parabola is y2 = 4ax Here, a = Distance of focus from vertex = 5 cm Now, Mirror is 45 cm Deep Hence, x-coordinate of point A = 45 x = 45 Putting x = 45 and a = 5 in (1) y2 = 4ax y2 = 4 × 5 ×45 y2 = 900 y = ± ﷐﷮900﷯ y = ± 𝟑𝟎 Hence, Point C is (0, 30) & Point D is (0, 30) Hence OC = 30 cm & OD = 30 cm Distance CD = OC + OD = 30 + 30 = 60 cm So, AB = CD = 60 cm

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.