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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?

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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onramps precal D:

No Anthony

hi pedro

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Did you know?

Did you know that a fireplace arch can be constructed in the shape of a semiellipse? In this construction, the opening of the arch has a height of 2 feet at the center and a width of 6 feet along the base. To sketch the outline of the semiellipse, the contractor cuts a string of a certain length and nails each end of the string along the base. 1. The total length of the string is equal to the circumference of the semiellipse, which can be calculated using the formula 𝜋 x (width/2 + height^2 / 8). Given that the width is 6 feet and the height is 2 feet, the total length of the string can be determined. 2. The string should be nailed into the base of the semiellipse at a distance equal to the semi-major axis, which is the half of the width. Therefore, the string should be nailed 3 feet away from the center of the base.