(Solved): Determine whether the equation represents an ellipse, a parabola, or a hyperbola. \[ 4 x+y^{2}+8 y ...

Determine whether the equation represents an ellipse, a parabola, or a hyperbola. \[ 4 x+y^{2}+8 y+8=0 \] ellipse parabola hyperbola If the graph is an ellipse, find the center, foci, and vertices. If it is a parabola, find the vertex, focus, and directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes. (Enter your answers for asymptotes as a comma-separated list of equations. If an answer does not exist, enter DNE.) center \[ \begin{array}{l} (x, y)=(1) \\ \text { focus }(x, y)=(\quad) \text { (smaller } x \text {-value or only focus) } \\ \text { focus }(x, y)=1 \quad \text { (larger } x \text {-value) } \\ \text { vertex }(x, y)=(\quad) \text { (smaller } x \text {-value or only vertex) } \\ \text { vertex } \quad(x, y)=(\quad)(\text { larger } x \text {-value }) \\ \end{array} \] length of the major axis length of the minor axis asymptotes directrix