math

A fireplace arch is to be constructed in form of a semiellipse. The opening is to have a height of 2 feet at the center and a width of 6 feet along the base. The contractor cuts a string of a certain length and nails each end of the string along the base in order to sketch the outline of the semiellipse.

1. What is the total length of the string?
2. How far from the center should the string be nailed into the base?

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  1. sum of distances from point on ellipse to foci = 2a where a is long semisaxis = 3
    so
    2 a = 6 = string length
    b = 2 (short semiaxis)

    center to focus =sqrt(3^2-2^2)
    = sqrt(5) = 2.236067977 feet which is tough with a ruler :)

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