The area of the circle centred at (1, 2) and passing through (4, 6), is

The radius of the circle centred at (1, 2) and passing through (4, 6) 

is given by $r=\sqrt{(4-1{)}^2+(6-2{)}^2}=5$ 

$\therefore \text{ Area }=\pi r^2=\pi (5{)}^2=25\pi \text{ sq. units }$