The length of the major axis of an ellipse is 20 units, and its foci are . Find the equation of the ellipse.

Let the equation of the required ellipse be

Given: Length of Major Axis = 20units …(i)

We know that,

Length of Major Axis = 2a …(ii)

∴ From eq. (i) and (ii), we get

2a = 20

⇒ a = 10

It is also given that,

Coordinates of foci = (±5√3, 0) …(iii)

We know that,

Coordinates of foci = (±c, 0) …(iv)

∴ From eq. (iii) and (iv), we get

c = 5√3

We know that,

c² = a² – b²

⇒ (5√3)² = (10)² – b²

⇒ 75 = 100 – b²

⇒ b² = 100 – 75

⇒ b² = 25

Substituting the value of a² and b² in the equation of an ellipse, we get