3) Graph and determine the coordinates of the center, the foci, the vertices, the eccentricity and the equation of the asymptotes of the following hyperbola

3. Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola or a degenerate conic. For ellipse: find center, foci, vertices, and length of the major and minor axes; For parabola: find the vertex, focus, and directrix; For hyperbola: find the center, foci, vertices, and asymptotes. Sketch the graph. (a) x² +6x+12y+9=0 (b) 2x² + y² = 2y +1 (c) 16x² (d) x² +16=4(y² +2x) -9y²-96x+288=0

Given the equation of an ellipse, find each of the following:  a) the center; b) the vertices; c) the foci, and d) the eccentricity.  Clearly identify which point is the center and which points are the vertices and which are the foci, and give the result for the eccentricity as a decimal, rounded to two decimal places if necessary.