Conic Sections Question 354
Question: 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
[MNR 1989]
Options:
A) $ 6,\ 2\sqrt{5} $
B) $ 6,\ \sqrt{5} $
C) $ 4,\ 2\sqrt{5} $
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
Given $ 2a=6,2b=4 $ i.e. , $ a=3,b=2 $
$ e^{2}=1-\frac{b^{2}}{a^{2}}=\frac{5}{9} $
therefore $ e=\frac{\sqrt{5}}{3} $
Distance between the pins $ =2ae=2\sqrt{5}cm $
Length of string $ =2a+2ae=6+2\sqrt{5}cm $ .
BETA
