We need to find the area of the circle passing through (- 2,6) and having a centre at (1,2).

We know that the radius of the circle is the distance between the centre and any point on the radius. So, we find the radius of the circle.

We know that the distance between the two points (x₁,y₁) and (x₂,y₂) is .

Let us assume r is the radius of the circle.

⇒

⇒

⇒

⇒ r = √25

⇒ r = 5

We know that the area of the circle is r².

⇒ Area(A) = π(5)²

⇒ A = π(25)

∴The area of the circle is 25π.