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The ends of a rod of length l move...

The ends of a rod of length `l` move on two mutually perpendicular lines. The locus of the point on the rod which divides it in the ratio 1 : 2 is

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The correct Answer is:
`4l^2`
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An iron rod of length 2l is sliding on two mutually perpendicular lines. Find the locus of the midpoint of the rod.

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Knowledge Check

  • A straight line segment of length I moves with its ends on two mutually perpendicular lines. Then the locus of the point which divides the line segment in the ratio 1 : 2 is

    A
    `9x^2+36y^2=4l^2`
    B
    `9x^2+36y^2=l^2`
    C
    `36x^2+9y^2=4l^2`
    D
    `36x^2+9y^2=4l^2`

  • The ends of a rod of lenght l move on the coordinate axes. The locus of the point on the rod which divides it in the ratio 1:2 is

    A
    `36x^(2)+9y^(2)=4l^(2)`
    B
    `36x^(2)+9y^(2)=l^(2)`
    C
    `9x^(2)+36y^(2)=4l^(2)`
    D
    `9x^(2)+36y^(2)=l^(2)`

  • A line of fixed length a + b moves so that its ends are always on two fixed perpendicular straight lines. Then the locus of a point which divides this line into portions of length a and b is

    A
    an ellipse
    B
    a parabola
    C
    a straight line
    D
    a hyperbola

    • Similar Questions

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    A line of fixed length (a+b) moves so that its ends are always on two perpendicular straight lines fixed. Prove that a marked point on the line , which divides this line in to portions of lengths a and b describes an ellipse when a=8 , b=12.

    A line of fixed length (a + b) moves so that its ends are always on two fixed perpendicular straight lines. Prove that a marked point on the line which divides this line into portions of length ‘a ’ and ‘b ’ describes an ellipse and also find the eccentricity of the ellipse when a = 8, b =12.

    A line of fixed length (a + b) moves so that its ends are always on two fixed perpendicular straight lines. Prove that a marked point on the line which divides this line into portions of length 'a' and 'b' describes an ellipse and also find the eccentricity of the ellipse when a = 8, b=12 .

    A rod PQ of length 2a slides with its ends on the axes. The locus of the circumcentre of DeltaOPQ is

    A rod AB os length 10 cms slides between two perpendicular lines OX ,OY . The maximum area of the DeltaOAB

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