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The ellipse (x^(2))/(a^(2))+(y^(2))/(b^(...

The ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` and the hyperbola `(x^(2))/(A^(2))-(y^(2))/(B^(2))=1` are given to be confocal and length of mirror axis of the ellipse is same as the conjugate axis of the hyperbola. If `e_1 and e_2` represents the eccentricities of ellipse and hyperbola respectively, then the value of `e_(1)^(-2)+e_(1)^(-2)` is

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The correct Answer is:
`(2)`
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The ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 and hyperbola x^(2)/A^(2) - y^(2)/B^(2) = 1 are given to be confocal and length of minor axis is of ellipse is same as the conjugate axis of the hyperbola . If e_(1)" and " e_(2) are the eccentricity of ellipse and hyperbola then value of 1/((e_(1))^(2)) + 1/((e_(2))^(2)) is ______

If the foci of the ellipse (x^(2))/(25)+(y^(2))/(b^(2))=1 and the hyperbola (x^(2))/(144)-(y^(2))/(81)=(1)/(25) coincide,then length of semi-minor axis is

Knowledge Check

  • If e_(1) , e_(2) " and " e_(3) the eccentricities of a parabola , and ellipse and a hyperbola respectively , then

    A
    ` e_(1) lt e_(2) lt e_(3)`
    B
    `e_(1) lt e_(3) lt e_(2)`
    C
    `e_(3) lt e_(1) lt e_(2)`
    D
    `e_(2) lt e_(1) lt e_(3)`

  • If e_(1) and e_(2) are the eccentricities of the hyperbola and its conjugate hyperbola respectively then (1)/(e_(1)^(2))+(1)/(e_(2)^(2)) is equal to

    A
    `5/4`
    B
    `4/5`
    C
    1
    D
    `1/2`

  • If e_(1) and e_(2) are the roots of the equation x^(2)-ax+2=0 where e_(1),e_(2) are the eccentricities of an ellipse and hyperbola respectively then the value of a belongs to

    A
    `(3,oo)`
    B
    `(2,oo)`
    C
    `(1,oo)`
    D
    `(-oo,1)cup(1,2)`

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    Let the foci of the hyperbola (X^(2))/(A^(2))-(y^(2))/(B^(2))=1 be the vertices of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and the foci of the ellipse be the vertices of the hyperbola. Let the eccentricities of the ellipse and hyperbola be e_(E) and e_(H) , respectively. Then match the following lists.

    Eccentricity of a hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is " (sqrt(41))/(5), the ratio of length of transverse axis to the conjugate axis is

    If e_(1) and e_(2) are the eccentricities of a hyperbola 3x^(2)-2y^(2)=25 and its conjugate, then

    If e_(1) and e_(2) are the eccentricities of a hyperbola 3x^(2)-3y^(2)=25 and its conjugate, then

    If e_(1)ande_(2) be the eccentricities of the hyperbola xy=c^(2)andx^(2)-y^(2)=c^(2) respectively then :

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