Find the equation of the ellipse, the co-ordinates of whose foci are `(0, pm4)` and eccentricity `(4)/(5)`

Explanation

Since the foci are on the y-axis, therefore the major axis is along the y-axis. So, equation of the ellipse is of the form `(x^(2))/(b^(2))+(y^(2))/(a^(2)) =1`
Given that c = 4 and `e = (4)/(5)`
we know that `e = ( c)/(a)`
`rArr a= 5" " i.e., a^(2) = 25`
Now, `c^(2) = a^(2) - b^(2)`
`rArr (4)^(2) = (5)^(2) - b^(2)`
`rArr b^(2) = 25 - 16`
`rArr b^(2) = 9`
`therefore` The required euation of the ellipse is `(x^(2))/(9) + (y^(2))/(25) =1`.