Final answer:
The area of the circle is 25π square units, calculated using the radius found through the distance formula and the area formula πr2.
Step-by-step explanation:
The area of a circle is calculated by the formula πr2, where r is the radius of the circle. To find the radius of the circle with its center at (1,2) and passing through the point (-2,6), we can use the distance formula which is √((x2-x1)2 + (y2-y1)2). The radius is the distance between the center and a point on the circle, and once the radius is known, we can easily calculate the area of the circle.
Step-by-Step Calculation
1. Calculate the radius (distance between the center and the point (-2,6)):
r = √((-2-1)2 + (6-2)2) = √(9+16) = √25 = 5.
2. Calculate the area of the circle using the formula πr2:
Area = π × (5)2 = π × 25 = 25π square units.