Find the equation of ellipse whose vertices are `(0,pm13)` and foci `(0,pm5)`.

Explanation

The vertices and foci of ellipse are on y-axis.
`:." "bgta`
Now co-ordinates of the vertices = `0,pmb)` and co-ordinates of foci `=(0,pmbe)`
`:.` b=13 and be=5
`:." "e=(5)/(13)`
and `a^(2)=b^(2)(1-e^(2))`
`=169(1-(25)/(169))=144`
`:.` Therefore, the equation of ellipse
`(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
`rArr" "(x^(2))/(144)+(y^(2))/(169)=1`.