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 .........

Answer

Length of string `=6+2sqrt(5),` Distance between pins `=2 sqrt(2)`

Explanation

Let the equation of the ellipse be `(x^(2))/(a^(2)) +(y^(2))/(b^(2))=1`
According to the equstions a=3 and b=2.
`rArre^(2)=1-(b^(2))/(a^(2))=1-(4)/(9)=(5)/(9)`
`:. E=(sqrt(5))/(3)`
From the difinition of the ellipse for any point P on the ellipse SP+S'P=2a where a S and S' are foc,
`:.` Length of the endless string =SP+S'P+SS'
=2a+ae
`=2xx3+2xx3(sqrt(5))/(3)`
`=6+2sqrt(5)`