Question

Identify the conic section represented by the equation left parenthesis x plus 1 right parenthesis squared plus left parenthesis y minus 2 right parenthesis squared equals 8.
(1 point)
Responses

circle
circle

ellipse
ellipse

hyperbola
hyperbola

parabola

Answer 1

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**.