An ellipse is described by using an endless string which is passed over two pins. If axes are 6 cm a

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10-2. Parabola, Ellipse, Hyperbola

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

A

$6,\;2\sqrt 5 $

B

$6,\;\sqrt 5 $

C

$4,\;2\sqrt 5 $

D

None of these

Solution

(d) Given $2a = 6,\,\,2b = 4$ $i.e.$ ,$a = 3,\,\,b = 2$

${e^2} = 1 – \frac{{{b^2}}}{{{a^2}}} = \frac{5}{9}$

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

Distance between the pins $ = 2ae = 2\sqrt 5\ cm$

Length of string $ = 2a + 2ae = 6 + 2\sqrt 5\ cm$.

Standard 11

Mathematics

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