Question

The ellipse `x^(2)/169+y^(2)/25=1` has the same eccentricity as the ellipse `x^(2)/a^(2)+y^(2)/b^(2)=1`. What is the ratio of a to b ?
A. `5//13`
B. `13//5`
C. `7//8`
D. `8//7`

Answer 1

Correct Answer - B
`"Given ellpse is "x^(2)/169+y^(2)/25=1`
`:.e=sqrt(1-25/169)=12/13`
Also, standard equation of ellipse is `x^(2)/a^(2)+y^(2)/b^(2)=1`
and eccentricity, `e=sqrt(1-b^(2)/a^(2))`
`:.12/13=sqrt(1-b^(2)/a^(2))rArrb^(2)/(a^(2))=1-144/169=25/169`
`rArr" "b/a=5/13rArra/b=13/5`