Find the equation if the ellipse whose axes are along the coordinate axes, vertices are `(+-5,0)` and foci at `(+-4,-0)dot`

Options

A. `9x^(2)+25y^(2)=1`
B. `9x^(2)+25y^(2)=225`
C. `25x^(2)+9y^(2)=225`
D. `25x^(2)+9y^(2)=1`

Answer

B

Explanation

Let the equation of the required ellipse be
`(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
the coordinates of its vertices and foci are `(+- a,0) and (+- ae,0) ` respectively
`therefore a=5 and ae=4implies e=(4)/(5)`
Now,
`b^(2)=a^(2)(1-e^(2))impliesb^(2)=25(1-(16)/(25))=9`
substiting the values of `a^(2) and b^(2) " in (i) we get " (x^(2))/(25)+(y^(2))/(9)=1,`
which is the equation of the required ellipse .