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A series of hyperbola are drawn having a...

A series of hyperbola are drawn having a common transverse axis of length 2a. Prove that the locus of point P on each hyperbola, such that its distance from the transverse axis is equal to its distance from an asymptote, is the curve `(x^2-y^2)^2 =lambda x^2 (x^2-a^2), ` then `lambda` equals

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Knowledge Check

  • The locus of a point which moves so that its distance from x-axis is double of its distance from y-axis it

    A
    `x=2y`
    B
    `y=2x`
    C
    `y=2x+3`
    D
    `x=5y+1`

  • If a point moves such that twice its distance from the axis of x exceeds its distance from the axis of y by 2, then its locus is

    A
    `x-2y=2`
    B
    `x+2y=2`
    C
    `2y-x=2`
    D
    `2y-3x=5`

  • Find the locus of a point whose distance from x-axis is equal the distance from the point (1, -1, 2) :

    A
    `y^(2)+2x-2y-4z+6=0`
    B
    `x^(2)+2x-2y-4z+6=0`
    C
    `x^(2)-2x+2y-4z+6=0`
    D
    `z^(2)-2x+2y-4z+6=0`

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