The eccentricity of the hyperbola `25x^(2)-9y^(2)=225` is . . .

Options

A. `(sqrt(34))/(3)`
B. `4`
C. `sqrt(34)`
D. `(sqrt(34))/(5)`

Answer

A

Explanation

We have equation of hyperbola
`25x^(2)-9y^(2)=225`
`implies(x^(2))/(9)-(y^(2))/(25)=1`
On comparing with `(x^(2))/(a^(2))-(y^(2))/(25)=1`
On comparing with `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`, we get
`a^(2)=9,b^(2)=25`
`therefore`Eccentricity, `e=sqrt(1+(b^(2))/(a^(2)))`
`=sqrt(1+(25)/(9))`
`=(sqrt(34))/(3)`