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Show that product of lengths of the perp...

Show that product of lengths of the perpendicular from any point on the hyperbola `x^(2)/(16)-y^(2)/(9)=1` to its asymptotes is `(144)/(25)`.

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Knowledge Check

  • The product of the lengths of the perpendiculars from any point of that hyperbola x^(2)-y^(2)=8 to its assymptotes is

    A
    2
    B
    3
    C
    4
    D
    8

  • The product of the perpendicular from any point on the hyperbola x^(2) //a^(2) -y^(2)//b^(2) =1 to its asymptotes is

    A
    ` (a^(2) +b^(2))/( a^(2)b^(2))`
    B
    ` (a^(2) -b^(2))/( a^(2)b^(2))`
    C
    ` (a^(2)b^(2))/(a^(2)+b^(2))`
    D
    `(a^(2) b^(2))/(a^(2)-b^(2))`

  • The product of lengths of the perpendiculars from the point of the hyperbola x^(2)-y^(2)=8 to its asymptotes is

    A
    2
    B
    3
    C
    4
    D
    8

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