A new bridge is to be constructed over a big river. The space between the supports must be 1000 feet; the height at the center of the arch needs to be 320 feet. The support could be in the shape of a parabola or a semi-ellipse. An empty tanker needs a 250 foot clearance to pass beneath the bridge. The width of the channel for each of the two plans must be determined to verify that the tanker can pass through the bridge.
Use the above information to answer the following questions:
a. Write the equation of a parabola with these characteristics
b. Write the equation of a semi ellipse with these characteristics
c. How wide is the channel that the tanker can pass through?

Solution Preview

(A)

-(x - 500)^2 = 4(70)(y - 320)

or

(x - 500)^2 = - 280(y - 320)

where p = 70 is the distance between the vertex and the focus

(B)

the equation is equation of the ellipse is

(x - 500)^2/ (500^2) + y^2 / (320^2) = 1

to find the equation of the semi-ellipse, solve for y and choose the positive square root ...

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