Find the equation of the ellipse whose vertices are at (±6, 0) and foci at (±4, 0).

Given: Vertices = (±6, 0) …(i)

The vertices are of the form = (±a, 0) …(ii)

Hence, the major axis is along x – axis

∴ From eq. (i) and (ii), we get

a = 6

⇒ a² = 36

and We know that, if the major axis is along x – axis then the equation of Ellipse is of the form of

Also, given coordinate of foci = (±4, 0) …(iii)

We know that,

Coordinates of foci = (±c, 0) …(iv)

∴ From eq. (iii) and (iv), we get

c = 4

We know that,

c² = a² – b²

⇒ (4)² = (6)² – b²

⇒ 16 = 36 – b²

⇒ b² = 36 – 16

⇒ b² = 20

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