Question

Find the equation of the ellipse that satisfies the given conditions: Vertices `(0,pm13)`, foci `(0,pm5)`

Answer 1

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