# Math

A fireplace arch is to be constructed in the form of a semi ellipse. The opening is to have a height of 3 feet at the center and a width of 8 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 semi ellipse.
a.) What is the total length of the string?
b.)How far from the center should the string be nailed into the base?

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1. He must nail the ends of the string at the focal points of the ellipse
For this ellipse:
c^2 + 3^2 = 4^2
c^2 = 7
c = √7

so one of the focal points is (√7, 0) , clear √7 units form the centre
using the definition of ellipse properties, the length of the string is 8 units

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Reiny

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