Question

The area of a circle centered at $(1,2)$ and passing through $(4,6)$ is

• A. $5\pi$ sq. units
• B. $15\pi$ sq. units
• C. $25\pi$ sq. units
  
• D. $30\pi$ sq. units
  

Answer 1

Answer: (C)

$25\pi$ sq. units

Coordinates of the centre of the circle $(x_1,y_1)=(1,2)$

and coordinates of the point through which it passes $(x_2,y_2)=(4,6)$.

We know that the radius of the circle $r=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}=\sqrt{{(4-1)}^2+{(6-2)}^2}=\sqrt{9+16}=5$

Therefore, the area of the circle

$\pi r^2=\pi {\left(5\right)}^2=25\pi$ sq. units