# 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 Length Of The String And Distance Between The Pins Are ____________

As we know:

$$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$$

Therefore,

a = 6cm and $$a^{2} = 36$$

b = 4 and $$b^{2} = 16$$

Therefore,$$b^{2} = a^{2} (1 – e^{2})$$

=$$e^{2} = 1 – \frac{b^{2}}{a^{2}} = 1$$

= $$\frac{16}{36} = \frac{5}{9}$$

Therefore,

$$e = \sqrt{\frac{5}{9}} = \sqrt{\frac{5}{3}}$$ $$ae = \frac{6 * \sqrt{5}}{3}$$

= $$2\sqrt{5}$$

Hence, the length of the string and distance between the pins are $$6 + 2\sqrt{5}, 2\sqrt{5}$$

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