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  • An ellipse is described by using an endless string which is passed over two pins. If the axes are 6 cm and 4 cm, the length of the string and distance between the pins are ____________.

An ellipse is described by using an endless string which is passed over two pins. If the axes are 6 cm and 4 cm, the length of the string and distance between the pins are ____________.

Answers (1)

Let equation of ellipse be \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1

a=3 and b=2

b2=a2(1-e2)

e2=1-4/9=5/9

e=\frac{\sqrt{5}}{3}

From the definition of the ellipse for any point P on the ellipse we have

SP+S'P=2a

Length of endless string=SP+S'P+SS'=2a+2ae=2(3)+2(3)*\frac{\sqrt{5}}{3}=6+2\sqrt{5}

 

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infoexpert22

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