The eccentricity of the ellipse `9x^2+25 y^2-18 x-100 y-116=0` is
a.`25//16` b. `4//5` c. `16//25` d. `5//4`

Explanation

`9x^2+25 y^2-18 x-100 y-116=0`

`implies 9(x^2-2x+1)+25(y^2-4y+4)=116+100+9`

`implies 9(x-1)^2+25(y-2)^2=225`

`implies{(x-1)^2}/25+{(y-2)^2}/9=1`

Here, `a=5,b=3`

And `e=sqrt{1-{b^2}/{a^2}}`

`implies e=sqrt{1-9/25}`

`implies e=4/5`