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Find the locus of the midpoint of the po...

Find the locus of the midpoint of the portion of a straight line distant p from the origin intercepted between the axes.

Text Solution

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The correct Answer is:
`p^(2)(x^(2)+y^(2))=4x^(2)y^(2)`
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The locus of the mid - points of the portion of the tangents of the ellipse (x^2)/2+(y^2)/1=1 intercepted between the coordinate axes is

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Knowledge Check

  • The locus of the midpoint of the portion of the line x cos alpha+y sin alpha=p intercepted between the axes is

    A
    `p^(2)(x^(2)+y^(2))=2x^(2)y^(2)`
    B
    `p^(2)(x^(2)+y^(2))=4x^(2)y^(2)`
    C
    `p^(2)(x^(2)+y^(2))=x^(2)y^(2)`
    D
    `p^(2)(x^(2)+y^(2))=16x^(2)y^(2)`

  • A variable line x/a+y/b=1 is such that a+b=10 . The locus of the midpoint of the portion of the line interecepted between the axes is

    A
    `x+y=10`
    B
    `10x+5y=1`
    C
    `x+y=5`
    D
    `5x+10y=1`

  • The locus of the middle point of the portion of a normal to the parabola y^(2)=4ax intercepted between the curve and the axis is

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

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    Explore conceptually related problems

    The locus of the midpoint of the protion of the line x cos alpha+y sin alpha=p where p is a constant, intercepted between the axes is

    p is the length of the perpendicular drawn from the origin upon a straight line then the locus of mid point of the portion of the line intercepted between the coordinate axes is

    The equation of the line passing through the point P(1, 2) such that P bisects the part intercepted between the axes is

    The locus of point of intersection of perpendicular straight lines which are at constant distance p from origin is

    A variable tangent to the ellipse (x^2)/(a^2) + (y^2)/(b^2)=1 makes intercepts on both the axes. The locus of the middle point of the portion of the tangent between the coordinate axes is

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