An ellipse is described by using an endless string which is passe… - Vidyadip

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
$4,2 \sqrt{5}$
✓
$6+2 \sqrt{5}, 2 \sqrt{5}$

✓

Answer

Correct option: D.

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

(D)
Given, $2 a =6,2 b=4$
i.e., $a=3, b=2$
Also, $e ^2=1-\frac{ b ^2}{ a ^2}=\frac{5}{9}$
$\Rightarrow e =\frac{\sqrt{5}}{3}$
∴ Distance between the pins $=2 ae =2 \sqrt{5} cm$
and length of string $=2 a +2 ae =6+2 \sqrt{5} cm$

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