The equation \((x + 1)^2 + (y - 2)^2 = 8\) represents a circle. This is evident because it is in the standard form of a circle's equation, \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center of the circle and \(r\) is the radius.
Thus, the correct response is circle.