Explanation

(c)
Given equation of circle can be rewritten as
$x^{2} + y^{2} - \frac{3}{2}x + 3y + 1 = 0$
Whose centre is $\left( \frac{3}{4}, - \frac{3}{2} \right)$
and radius, $r = \sqrt{\frac{9}{16} + \frac{9}{4} - 1} = \sqrt{\frac{29}{16}}$
Area of circle $= \pi r^{2} = \frac{29\pi}{16}$
$\Rightarrow$ Area of required circle$= 2 \times \frac{29\pi}{16} = \frac{29\pi}{8}$
Let $R$ be the radius of required circle
$\therefore\ \ \ R^{2} = \frac{29}{8}$
Now, equation of circle is $\left( x - \frac{3}{4} \right)^{2} + \left( y + \frac{3}{2} \right)^{2} = \frac{29}{8}$
$\Rightarrow \ 16x^{2} + 16y^{2} - 24x + 48y - 13 = 0$