Question

Find the equation of the ellipse that satisfies the given conditions: Length of major axis 26, foci `(pm5,0)`

Answer 1

Here, foci `-=(pm5,0)`, which lie on x-axis.
`:.` Given, major axis 2a=26
`rArr" "a=13" "a^(2)=169`
and `b^(2)=a^(2)(1-e^(2))`
`=a^(2)-a^(2)e^(2)`
`=169-(5)^(2)=144`
Now, equation of ellipse
`(x^(2))/(a^(2))+(y^(2))/(b^(2))=1rArr(x^(2))/(169)+(y^(2))/(144)=1`