Question

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

5x² + 4y² = 1.

Answer 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

⇒ Coordinates of foci (0, ±be)

⇒ Length of latus rectum = \(\cfrac{2a^2}b\)

Here a² = 1/5 and b² = 1/4, b² > a²

⇒ Length of latus rectum (L) = \(\cfrac{2(\frac15)}{\frac12}\)

⇒ L = \(\cfrac45\)

∴ The eccentricity is \(\sqrt{\cfrac15}\), foci are \(\left(0,\pm\cfrac{1}{2\sqrt5}\right)\) and length of the latus rectum is \(\cfrac45\).