Given that we need to find the equation of the ellipse whose length of major axis is 26 and foci (±5,0).

Let us assume the equation of the ellipse as (a²>b²).

We know that length of the major axis is 2a

⇒ 2a = 26

⇒ a = 13

⇒ a² = 169

We know that foci = (±ae,0)

⇒ ae = 5

⇒ 13e = 5

⇒

We know that eccentricity

⇒

⇒

⇒

⇒ b² = 144

The equation of the ellipse is

⇒

∴ The equation of the ellipse is .