The eccentricity of the hyperbola `16x^(2)-9y^(2)=1` is?

Options

A. `3/5`
B. `5/3`
C. `4/5`
D. `5/4`

Answer

B

Explanation

`because16x^(2)-9y^(2)=1`
`because16x^(2)-9y^(2)=1`
`"or "x^(2)/(1/4)^(2)-y^(2)/(1/4)^(2)=1`
`"Comparing with "x^(2)/a^(2)-y^(2)/(1/3)^(2)=1`
`:. A^(2)=1/16`
`& b^(2)=1/9`
`because e=sqrt(1+b^(2)/a^(2))`
`:.e=sqrt(1+(1/9)/(1/16))`
`rArr" "e=5/3`