Answer
$$\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{{21}} = 1$$
Work Step by Step
$$\eqalign{
& {\text{ellipse with foci at }}\left( { \pm 2,0} \right){\text{ and major axis with length 1}}0 \cr
& {\text{The coordinates of the foci are }}\left( { \pm c,0} \right),{\text{ then}} \cr
& {\text{The equation of the ellipse is of the form }}\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1 \cr
& {\text{Major axis length }}2a \cr
& 2a = 10 \to a = 5 \cr
& {\text{Foci at }}\left( { \pm 2,0} \right),\,\,\left( { \pm c,0} \right) \to c = 2 \cr
& {b^2} = {a^2} - {c^2} \cr
& {b^2} = {5^2} - {2^2} = 21 \cr
& \cr
& {\text{The equation of the ellipse is}} \cr
& \frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{{21}} = 1 \cr} $$
