Question

Find the equation of the ellipse that satisfies the given conditions: Vertices `(pm5,0)`, foci `(pm4,0)`

Answer 1

Vertices `-=(pm5,0)`, foci `(pm4,0)`
`because` The y-coordinate of each of vertices and foci are zero.
`:.` The major axis of the ellipse will be along x-axis.
Now, a=5 and ae=4
and `b^(2)=a^(2)(1-e^(2))`
`=a^(2)-a^(2)e^(2)`
`=5^(2)-4^(2)=9`
Equation of ellipse
`(x^(2))/(a^(2))+(y^(2))/(b^(2))=1 rArr(x^(2))/(25)+(y^(2))/(9)=1`