Determine the general form of the equation for the circle x^2 + (y + 1) ^2 = 2.

x² + y² + 2y - 1 = 0

Step-by-step explanation:

The general form of the equation for the circle:

x² + y² + ax + by + c = 0

Where: a, b and c are constants.

For the given equation:

x² + (y + 1) ² = 2

∴ x² + (y + 1) (y+1) = 2

∴ x² + y² + 2y + 1 = 2 ⇒ subtract 2 from both sides

∴ x² + y² + 2y + 1 - 2 = 2 - 2

∴ x² + y² + 2y - 1 = 0

So, the general form of the equation for the circle:

x² + y² + 2y - 1 = 0