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Q. AN ELLIPSE IS DESCRIBED BY USING AN ENDLESS STRING WHICH PASSED OVER TWO PINS.IF THE AXES ARE 6 CM AND 4 CM . THE NECESARRY LENGHT OF THE STRING AND THE DISTANCE BETWEEN THE PINS RESPECTIVELY IN CMS ARE

Q. AN ELLIPSE IS DESCRIBED BY USING AN ENDLESS STRING WHICH PASSED OVER TWO PINS.IF THE AXES
ARE 6 CM AND 4 CM . THE NECESARRY LENGHT OF THE STRING AND THE DISTANCE BETWEEN THE PINS RESPECTIVELY IN CMS ARE

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
8 years ago
Ans:
Hello Student,
Please find answer to your question below

According to definition of the ellipse, string length should be equal to major axis.
And the two pins are at the focus of the ellipse.
Major Axis (2a):
6 cm
Minor Axis (2b):
4 cm
String Length:
6 cm
Eccentricity (e):
e = \sqrt{1- \frac{b^{2}}{a^2}}
e = \sqrt{1- \frac{2^{2}}{3^2}}
e = \sqrt{\frac{5}{9}}
e = \frac{\sqrt{5}}{3}
Distance b/w two pins:
2ae
6.\frac{\sqrt{5}}{3}
2\sqrt{5}

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