Question
Asked Dec 24, 2019
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Two large airship hangars were built in Orly, France, in the early 1900s but were destroyed in World War II by American aircraft. The hangars were 175 m in length, 90 m wide, and 60 m high and were formed by a series of parabolic arches.

a. Set up a coordinate system with (0, 0) at the vertex of one of the arches and write an equation of the parabola.

b. What is the focal length of an arch?

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Expert Answer

Step 1

(a). It is given that, the length of hangars is 175 m, the width of the hangers is 90 m and the height of the hangers is 60 m.

The vertex of the parabola is (0, 0).

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Note that, the standard equation of parabola is (x – h) = 4p(y–k), where vertex is (h, k) Substitute (0, 0) for (h, k) in (x – h) = 4p(y–k). (x –0) = 4p(y- 0) x² = 4 py

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Step 2

Since the width of the parabola is 90, which means the points that lies on the parabola.

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The point (45, -60) satisfies the equation x = 4 py Substitute 45 for x and -60 for y in x² = 4 py. (45) = 4p(-60) 2025 = -240p 2025 p = -. 240 135 16

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Step 3

...
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135 x² = 16 135 x? 135 y with vertex (0, 0). 4 Thus, the equation of the parabola is x

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