Determine the general form of the equation for the circle x2 + (y + 1)2 = 2.
The general form of the equation for a circle is (x - h)^2 + (y - k)^2 = r^2, where (h,k) is the center of the circle and r is the radius.
Given the equation x^2 + (y + 1)^2 = 2, we can rewrite it in general form by expanding the squares:
x^2 + y^2 + 2y + 1 = 2
Rearranging the terms:
x^2 + y^2 + 2y = 1
We can complete the square for the y terms by adding (2/2)^2 = 1 to both sides of the equation:
x^2 + y^2 + 2y + 1 = 1 + 1
x^2 + y^2 + 2y + 1 = 2
(x^2 + y^2 + 2y) + 1 = 2
(x^2 + y^2 + 2y + 1) = 2
(x^2 + (y + 1)^2) = 2
So, the general form of the equation for the circle is x^2 + (y + 1)^2 = 2.