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10.2 parabola,ellipse,hyperbola — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS10.2 parabola,ellipse,hyperbola1 Mark
MCQ
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 $
  • ✓
    None of these
✓

Answer

Correct option: D.
None of these
d
(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$.

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