Find the eccentricity, coordinates of foci, length of the latus - rectum of the following ellipse:

4x² + 9y² = 1

Given the equation of the ellipse is 4x² + 9y² = 1.

We need to find the eccentricity, coordinates of foci and length of latus rectum.

Given equation can be rewritten as .

We know for the ellipse (a²>b²)

⇒

⇒ Coordinates of foci (±ae,0)

⇒ Length of latus rectum =

Here and , a²>b²

⇒

⇒

⇒

⇒

⇒

⇒

⇒ Length of latus rectum (L) =

⇒

∴ The eccentricity is , foci are and length of the latus rectum is .