Last updated at Dec. 8, 2016 by Teachoo

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 semi−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 = 𝟖𝟐 = 4 Now, equation of ellipse 𝑥2𝑎2 + 𝑦2𝑏2 = 1 Putting values of a & b 𝑥242 + 𝑦222 = 1 𝒙𝟐𝟏𝟔 + 𝒚𝟐𝟒 = 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 − 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) 𝑥216 + 𝑦24 = 1 (2.5)216 + 𝑦24 = 1 6.2516 + 𝑦24 = 1 6.25 + 4𝑦216 = 1 6.25 + 4y2 = 16 4y2 = 16 − 6.25 4y2 = 9.75 y2 = 9.754 y = 9.754 y = 9.752 y = 3.122 y = 1.56 (approx) Hence, the required height is 1.56 m (approx)

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Davneet Singh

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.