Find an equation of the circle that has center (-2, 1) and passes through the origin.
To find the equation of a circle, we need to know the coordinates of its center and either the radius or a point on the circle. In this case, we have the center (-2, 1) and a point on the circle, which is the origin (0, 0).
The general equation of a circle with center (h, k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2
Substituting the given values, we get:
(x - (-2))^2 + (y - 1)^2 = r^2
(x + 2)^2 + (y - 1)^2 = r^2
Since the circle passes through the origin (0, 0), we can substitute these values into the equation:
(0 + 2)^2 + (0 - 1)^2 = r^2
2^2 + (-1)^2 = r^2
4 + 1 = r^2
5 = r^2
Therefore, the equation of the circle is:
(x + 2)^2 + (y - 1)^2 = 5