For simplicity, let's assume the major axis lies along thex-axis, where the foci are at (-c,0) and (c,0), and .

If the product of the distances from the point (-3,1) to the foci is 6, then we may state:

Squaring gives:

Now solve this for .

Next, the equation of the ellipse may be written:

Since the ellipse passes through (-3,1), we may write:

where .

Using the value you found for , you may now solve for to find the equation of the ellipse.