find the equation of the ellipse whose focus are (1,1) and (6,6)

Question

find the equation of the ellipse whose focus are  (1,1) and (6,6)

anonymous · Answer

How are you going with this question? Have you attempted the question yet, if so, could you show us what you've done?

terenzreignz · Answer

Also, a pair of foci are generally not sufficient to determine a particular ellipse

anonymous · Answer

There is the theory states that the sum of distances of any point on the ellipse to the 2 focus is equal to a fixed-length equal to the major axis = 2a and  from this geometrical  characteristic can get the equation in one line but I wonder Is there any other way to get it without the theory it was a question in my final exam

amistre64 · Answer

since the line between your foci is not horizontal, nor vertical, it will be a rotated conic that takes a general form:

Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0

im not proficient at the details, but you could move this by a rotation about the origin by some fancy xy substitutions.