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Misc 4 - Chapter 11 Class 11 Conic Sections - Part 2
Misc 4 - Chapter 11 Class 11 Conic Sections - Part 3 Misc 4 - Chapter 11 Class 11 Conic Sections - Part 4

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Transcript

Misc 4 An arch is in the form of semi ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end. The arch is in form of semiโˆ’ellipse It is 8m wide & 2m high Let AB = width of semi-ellipse = 8 m & CO = Height of semi-ellipse = 2 m We know that Length of Major axis of ellipse = 2a AB = 2a 8 = 2a 2a = 8 a = ๐Ÿ–/๐Ÿ = 4 Length of semi-minor axis = b CO = b 2 = b b = 2 Now, equation of ellipse ๐‘ฅ2/๐‘Ž2 + ๐‘ฆ2/๐‘2 = 1 Putting values of a & b ๐‘ฅ2/4^2 + ๐‘ฆ2/2^2 = 1 ๐’™๐Ÿ/๐Ÿ๐Ÿ” + ๐’š๐Ÿ/๐Ÿ’ = 1 We need to find the height of arch at a point 1.5 m from one end. Let y be the height of arch from a point 1.5 from one end. Now, width of arch is (4 โˆ’ 1.5m) = 2.5m So, point P (2.5, y) lie on ellipse it will satisfy equation of ellipse Putting x = 2.5 & y = y in (1) ๐‘ฅ2/16 + ๐‘ฆ2/4 = 1 ((2.5)2)/16 + ๐‘ฆ2/4 = 1 6.25/16 + ๐‘ฆ2/4 = 1 (6.25 + 4๐‘ฆ^2)/16 = 1 6.25 + 4y2 = 16 4y2 = 16 โˆ’ 6.25 4y2 = 9.75 y2 = 9.75/4 y = โˆš9.75/2 y = 3.12/2 y = 1.56 (approx) Hence, the required height is 1.56 m (approx)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.