To find the length of the latus rectum of the ellipse, we first recognize that the foci of the ellipse are given as and . This indicates that the major axis is aligned along the -axis.

Calculate the distance between the foci:

The formula involving the distance between the foci and the eccentricity is:

Here, the eccentricity is given as . Thus, we can solve for :

Determine :
Using the relationship between eccentricity, semi-minor axis , and semi-major axis :

Solving for :

Thus, .

Compute the length of the latus rectum:
The formula for the length of the latus rectum
is:

Substituting the known values:

Therefore, the length of the latus rectum of the ellipse is .

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