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

• A. 6, 2$\sqrt{5}$
• B. 6, $\sqrt{5}$
• C. 4, 2$\sqrt{5}$
• D. None

Answer 1

Answer: (D)

None

Answer 2

Given 2a = 6, 2b = 4 i.e., a = 3, b = 2

e² = 1 - $\frac{b^{2}}{a^{2}} = \frac{5}{9} \Rightarrow e = \frac{\sqrt{5}}{3}$

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

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