The perimeter of the elliptical table is given by the path traced with the
string attached to the foci of the ellipse.
- The distance between the two thumbtacks is 2·√(5)
Reasons:
The shape of the table top = An ellipse
The dimensions of the plywood = 4 foot by 6 foot
Required:
The distance between the thumbtacks of the largest possible ellipse
Solution:
The major axis of the largest possible axis = 6 foot
The minor axis of the ellipse = 4 foot
[tex]The \ semi \ major \ axis, \ a = \dfrac{6}{2} = 3[/tex]
[tex]The \ semi \ minor \ axis, \ b = \dfrac{4}{2} = 2[/tex]
Which gives;
The focus, c² = a² - b²
Therefore;
c² = 3² - 2² = 5
c = √(5)
The distance between the two thumbtacks = c - (-c) = c + c = 2·c
Therefore;
The distance between the two thumbtacks = 2·√(5)
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