Complete the square to determine if equation is an ellipse, parabola, hyperbola, or a degenerate conic. Y^2=4(x+2y)
To determine if the equation describes an ellipse, parabola, hyperbola, or a degenerate conic, we can rewrite the equation in the standard form for each type of conic.
Given equation: y^2 = 4(x + 2y)
Rearrange the equation to complete the square:
y^2 - 4y = 4x
y^2 - 4y + 4 = 4x + 4
(y - 2)^2 = 4(x + 1)
Comparing the completed square form with the general form of the standard equation for the conics, we see that it resembles the equation of a parabola:
(y - k)^2 = 4a(x - h)
Therefore, the given equation describes a parabola.