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If e1, e2, are the eccentricities of a h...

If `e_1, e_2`, are the eccentricities of a hyperbola, its conjugate hyperbola, prove that `(1)/(e_1^2)+(1)/(e_2^2)=1`.

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Knowledge Check

  • If e1 and e2 are the eccentricities of a hyperbola and its conjugates then ,

    A
    `e_1^(2) +e_2^(2) =3`
    B
    ` e_1 +e_2 =4`
    C
    ` e_1^(2) +e_2^(2) =e_1^(2) e_2^(2) `
    D
    ` e_1=e_2 `

  • If a,b are eccentricities of a hyperbola and its conjugate hyperbola then a^(-2)+b^(-2)=

    A
    4
    B
    1
    C
    `a^(2)b^(2)`
    D
    `a^(-2)b^(2)`

  • If the eccentricities of a hyperbola is sqrt3 ,then the eccentricity of its conjugates hyperbola is

    A
    `sqrt2`
    B
    ` sqrt3`
    C
    ` sqrt(3//2)`
    D
    ` 2sqrt3 `

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    I : If e and e' are the eccentricity of the hyperbola x^(2) //a^(2) -y^(2)//b^(2) =1 and its conjugate hyperbola the value of 1//e^(2) +1//e'^(2) is 1 II : If e and e_1 are the eccentricity of the hyperbola xy =c^(2) , x^(2) -y^(2) =c^(2) " then" e^(2)+ c_1^(2) is equal to 4

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