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The asymptotes of a hyperbola are y = pm...

The asymptotes of a hyperbola are `y = pm b/a x`, prove that the equation of the hyperbola is `x^(2)/a^(2) - y^(2)/b^(2) = k ` , where k is any constant.

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Knowledge Check

  • The asymptotes of the hyperbola xy–3x–2y=0 are

    A
    `x – 2 = 0" and "y – 3 = 0`
    B
    `x – 3 = 0" and "y – 2 = 0`
    C
    `x + 2 = 0" and "y + 3 = 0`
    D
    `x + 3 = 0" and "y + 2 = 0`

  • If the asymptotes of the hyperbola perpendicular to the asymptotes of the hyperbola (x^(2))/(49)-(y^(2))/(b^(2)) =1 then

    A
    `7apm6b=0`
    B
    `6a+7b=0`
    C
    `a^(2)-b^(2)=1`
    D
    a-b=1

  • The auxiliary equation of circle of hyperbola (x ^(2))/(a ^(2)) - (y^(2))/(b ^(2)) =1, is

    A
    `x ^(2) + y^(2) =a ^(2)`
    B
    `x ^(2) + y ^(2) = b^(2)`
    C
    `x ^(2) + y^(2) =a ^(2) + b ^(2)`
    D
    `x ^(2) + y^(2)=a^(2) - b^(2)`

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    Statement -1 : The lines y = pm b/a xx are known as the asymptotes of the hyperbola x^(2)/a^(2) - y^(2)/b^(2) - 1 = 0 . because Statement -2 : Asymptotes touch the curye at any real point .

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