find the equation of the ellipse in the following cases:

Vertices (± 6, 0), foci (± 4, 0)

Given that we need to find the equation of the ellipse whose vertices are (±6,0) and foci (±4,0).


Let us assume the equation of the ellipse as (a2>b2).



We know that vertices of the ellipse are (±a,0)


a = 6


a2 = 36


We know that foci = (±ae,0)


ae = 4


6e = 4



We know that eccentricity





b2 = 20


The equation of the ellipse is




5x2 + 9y2 = 180


The equation of the ellipse is 5x2 + 9y2 = 180.


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