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(D) The length of the string used to draw an ellipse with pins at the foci is equal to the sum of the major axis and the distance between the foci.Giv

Vedclass · Accepted Answer

$6 + 2\sqrt{5}, 2\sqrt{5}$

Vedclass · Answer

(D) The length of the string used to draw an ellipse with pins at the foci is equal to the sum of the major axis and the distance between the foci.Given the major axis $2a = 6 \ cm$,so $a = 3 \ cm$.Given the minor axis $2b = 4 \ cm$,so $b = 2 \ cm$.The eccentricity $e$ is given by $e = \sqrt{1 - \frac{b^2}{a^2}} = \sqrt{1 - \frac{4}{9}} = \sqrt{\frac{5}{9}} = \frac{\sqrt{5}}{3}$.The distance between the pins (foci) is $2ae = 2 	imes 3 	imes \frac{\sqrt{5}}{3} = 2\sqrt{5} \ cm$.The length of the string is $2a + 2ae = 6 + 2\sqrt{5} \ cm$.

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 necessary length of the string and the distance between the pins respectively in $cm$,are

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