Find the equation of the ellipse whose vertices are `(+-13 ,0)`and foci are `(+-5,0)`.

Explanation

The vertices and foci of the ellipse are on x-axis, therefore
let the equation of ellipse be `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` where `agtb` Now given that, vertices `=(pma,0)=(pm13,0)`
a=13
and `foci=(pmae,0)=(pm5,0)`
`rArr" "ae=5`
`rArr" "13e=5`
`rArr" "e=(5)/(13)`
Now `b^(2)=a^(2)(1-e^(2))`
`=169(1-(25)/(169))=144`
`:.` Equation of ellipse
`(x^(2))/(169)+(y^(2))/(144)=1`.