A fireplace arch is to be constructed in the form of a semiellipse. 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 semiellipse.

Question

A fireplace arch is to be constructed in the form of a semiellipse. 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 semiellipse.

a.) What is the total length of the string?

b.) How far from the center should the string be nailed into the base?

oobleck · Answer

recall that an ellipse with semiaxes a and b and focus at c has the property that a^2 = b^2 + c^2 The sum of the distances from (x,y) on the ellipse is 2a.