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Find the distance between the directrices of the ellipse `(x^2)/(36)+(y^2)/(20)=1.`

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`x^2/36+y^2/20=1`
`a^2=36,b^2=20`
`a=pm6,b=pm2sqrt5`
`e=sqrt(36-20)/6=2/3`
`e=2/3`
Distance between directrics=6/(2/3)=9.
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Knowledge Check

  • If the distance between the foci and the distance between the directrices of the hyperbola x^(2)/(a_2 )-y^(2)/b_2 =1 are in the ratio 3:2

    A
    `sqrt2:1`
    B
    `sqrt3:sqrt2`
    C
    `1:sqrt2`
    D
    `2:1`

  • Find the eccentricity of the ellipse (x^2) /( 36 ) + (y^2)/( 16) = 1 .

    A
    `(6)/( sqrt20)`
    B
    `(sqrt6)/( 20)`
    C
    `(sqrt20)/( 6)`
    D
    `(20)/( sqrt6)`

  • Distance between the directrices of the hyperbola (x^(2))/(49)-(y^(2))/(16) =1 is

    A
    `sqrt(65)/(7)`
    B
    `(49)/sqrt(65)`
    C
    `sqrt(33)/(4)`
    D
    `(98)/sqrt(65)`
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