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 of these

Answer 1

Answer: (D)

None of these

Answer 2

2a = 6, 2b = 4

̃ a = 3 ̃ b = 2

e = $\sqrt{1 - \frac{4}{9}}$ = $\frac{\sqrt{5}}{3}$

2ae = 2 × 3 × $\frac{\sqrt{5}}{3}$ = $2\sqrt{5}$

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