For a conic, the eccentricity (e) between 0 and 1 will make this an ellipse.
Since the foci are located at (6,1) and (6,11), the distance between foci is 12 units = 2c.
The eccentricity is related to half of this distance and half of the length of the major axis of the ellipse (2a).
e = c/a
We also have a^{2}b^{2 }= c^{2} for an ellipse.
So c = 6, which makes a = 10, which makes b = 8.
Since the center of the ellipse is at (6,5), the equation for the ellipse is (y+5)^{2}/a^{2} + (x6)^{2}/b^{2} = 1
or (y+5)^{2}/100+(x6)^{2}/64=1
8/28/2014

Francisco P.