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The eccentricity of the hyperbola 16x^(2...

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

A

`3/5`

B

`5/3`

C

`4/5`

D

`5/4`

Text Solution

Verified by Experts

The correct Answer is:
B
`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`
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Knowledge Check

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

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

  • The eccentricity of the hyperbola x ^(2) - y^(2) =25 is

    A
    `sqrt2`
    B
    ` (1)/(sqrt2)`
    C
    `2`
    D
    `1+sqrt2`

  • The eccentricity of the hyperbola 9y^(2)-4x^(2)=36 is

    A
    `(5)/(2)`
    B
    `(sqrt(7))/(2)`
    C
    `(sqrt(13))/(2)`
    D
    2

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