Q. 95.0( 3 Votes )

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

4x^{2} + 9y^{2} = 1

Answer :

Given the equation of the ellipse is 4x^{2} + 9y^{2} = 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 (a^{2}>b^{2})

⇒

⇒ Coordinates of foci (±ae,0)

⇒ Length of latus rectum =

Here and , a^{2}>b^{2}

⇒

⇒

⇒

⇒

⇒

⇒

⇒ Length of latus rectum (L) =

⇒

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

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