Answer:
Explanation:
To find the area of the circle passing through the points (-8,0), (0,8), and (12,0), we can first find the center and radius of the circle using the following steps:
Find the midpoint of the line segment connecting any two of the given points to get the center of the circle.
Midpoint of (0,8) and (12,0):
x-coordinate: (0 + 12)/2 = 6
y-coordinate: (8 + 0)/2 = 4
Center: (6, 4)
Find the distance between the center of the circle and any one of the given points to get the radius of the circle.
Distance between (6,4) and (-8,0):
sqrt((6 - (-8))^2 + (4 - 0)^2) = sqrt(196 + 16) = sqrt(212)
Radius: sqrt(212)
Now that we have the center and radius of the circle, we can find the area of the circle using the formula:
Area = pi * radius^2
Area = pi * (sqrt(212))^2
Area = pi * 212
Area = 665.36 (approx)
Therefore, the area of the circle passing through the points (-8,0), (0,8), and (12,0) is approximately 665.36 square units.