Answer:
(1,2): Interior
(2,0): On
(3,2): Exterior
Explanation:
The circle equation is (x+1)^2 + y^2 = 9
To know if a point is inside, outside or on a circle, we first calculate the distance from this point to the center of the circle, using this equation:
d = sqrt(dx^2 + dy^2), where
d is the distance between the points,
dx is the difference in x axis between the points,
dy is the difference in y axis between the points.
The circle generic equation is (x−a)2 + (y−b)2 = r^2, where the point (a,b) is the circle's center.
So, looking at our circle equation, we know that the center is at (-1,0), and its radius is 3.
Now, we calculate the distance from our 3 points to the center of the circle:
point (1,2): dx = (1-(-1)) = 2, dy = 2-0 = 2, d = sqrt(2^2 + 2^2) = sqrt(8) = 2.8284
As this distance is lesser than the circle radius, this point is INTERIOR to the circle
point (2,0): dx = (2-(-1)) = 3, dy = 0-0 = 0, d = sqrt(3^2 + 0^2) = sqrt(9) = 3
As this distance is equal the circle radius, this point is ON the circle
point (3,2): dx = (3-(-1)) = 4, dy = 2-0 = 2, d = sqrt(4^2 + 2^2) = sqrt(20) = 4.4721
As this distance is greater than the circle radius, this point is EXTERIOR to the circle.