Find the eccentricity, coordinates of foci, length of the latus - rectum of the following ellipse:
5x2 + 4y2 = 1
Given the equation of the ellipse is 5x2 + 4y2 = 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 (b2>a2)
⇒
⇒ Coordinates of foci (0,±be)
⇒ Length of latus rectum =
Here and
, b2>a2
⇒
⇒
⇒
⇒
⇒
⇒ Length of latus rectum (L) =
⇒
∴ The eccentricity is , foci are
and length of the latus rectum is
.