Explanation

(b)
Given, $x^{2} + y^{2} - 7x + 9y + 5\text{=}0$
$\therefore R = \sqrt{\left( \frac{- 7}{2} \right)^{2} + \left( \frac{9}{2} \right)^{2} - 5}$
$= \sqrt{\frac{49}{4} + \frac{81}{4} - 5} = \frac{\sqrt{110}}{2}$
In $\mathrm{\Delta}OAB,\ \cos{30{^\circ}} = \frac{AB}{R}\ \Rightarrow \frac{\sqrt{3}}{2} = \frac{AB}{\frac{\sqrt{110}}{2}}$
[image:11_image26.emf]
$\Rightarrow \ \frac{\sqrt{330}}{4} = AB$
$\therefore Length\ AC = \frac{\sqrt{330}}{2}$
$\therefore\ Area\ of\ equilateral\ \mathrm{\Delta} = \frac{\sqrt{3}}{4}(a)^{2}$
$= \frac{\sqrt{3}}{4} \times \frac{330}{4} = \frac{165\sqrt{3}}{4}sq\ units$