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Chapter 10: Q 69. (page 655)

Semi elliptical Arch Bridge An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 20meters wide. The center of the arch is 6meters above the center of the river. See the figure. Write an equation for the ellipse in which the x-axis coincides with the water level and the y-axis passes through the center of the arch.

Short Answer

Expert verified

The equation for the ellipse isx2100+y236=1.

Step by step solution

01

Step 1. Given information.

From figure we have major axis equal to 20m.

The major axis of an ellipse is 2a.

So,

2a=20a=10

From figure the semi minor axis is b=6

The x-xis coincide with the water level and y-axis passes through the center of the arch. The center of the ellipse is (0,0)

02

Step 2. Equation of the ellipse.

Substitute a=10and b=6in the equation x2a2+y2b2=1we get.

x2102+y262=1x2100+y236=1

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