
Ellipse: Standard Form
Horizontal: a^{2} > b^{2} If the larger denominator is under the "x" term, then the ellipse is horizontal. center (h, k) a = length of semimajor axis b = length of semiminor axis vertices: (h + a, k), (h  a, k) covertices: (h, k + b), (h, k  b) [endpoints of the minor axis] c is the distance from the center to each focus. foci: (h + c, k), (h  c, k)
0 < e < 1 for an ellipse
Vertical: a^{2} > b^{2} If the larger denominator is under the "y" term, then the ellipse is vertical. center (h, k) a = length of semimajor axis b = length of semiminor axis vertices: (h, k + a), (h, k  a) covertices: (h + b, k), (h  b, k) [endpoints of the minor axis] c is the distance from the center to each focus. foci: (h, k + c), (h, k  c)
0 < e < 1 for an ellipse
Ax˛ + By˛ + Cx + Dy + E = 0 1) A & B have the same sign (both positive or both negative) 2) A & B are different numbers (if they were the same, this would be a circle). 
