An arch of a bridge is semi-elliptical with major axis horizontal. If the length the base is 9 meter and the highest part of the bridge is 3 meter from the horizontal; the best approximation of the he

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An arch of a bridge is semi-elliptical with major axis horizontal. If the length the base is 9 meter and the highest part of the bridge is 3 meter from the horizontal; the best approximation of the height of the arch. 2 meter from the centre of the base is

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The equation of the ellipse is ( 2 9 ​ ) 2 x 2 ​ + 9 y 2 ​ = 1 Where centre is assumed as origin and base as x -axis. Put x = 2 , we get 81 16 ​ + 9 y 2 ​ = 1 ⇒ y = 3 65 ​ ​ ≈ 3 8 ​ m (approximately)

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