Explanation

(c)
Since, the centre of circle is (1, 2) and this circle passes through (4, 6)
$\therefore$ Radius of circle=Distance between (1, 2) and (4, 6)
$= \sqrt{(4 - 1)^{2} + (6 - 2)^{2}}$
$= \sqrt{9 + 16} = \sqrt{25} = 5$
Hence area of circle$= \pi r^{2}$
$= \pi 5^{2} = 25\pi\ sq\ units$