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A line of fixed length a + b moves so th...

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

Text Solution

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The correct Answer is:
A
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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`

  • A line AB of length 2l moves with the end A always on the x-axis and the end B on the line y = 6x. The equation of the locus of the middle point of AB is

    A
    `9x^(2)+10y^(2)-6xy-9l^(2)=0`
    B
    `9x^(2)-10y^(2)+6xy+9l^(2)=0`
    C
    `9x^(2)+10y^(2)+6xy+9l^(2)=0`
    D
    `9x^(2)-10y^(2)-4xy+6l^(2)=0`

  • If p_(1), p_(2) are the perpendicular distances from the origin to the two perpendicular straight lines then the locus of the point of intersection of the lines is

    A
    `x^(2)+y^(2)=p_(1)^(2)+p_(2)^(2)`
    B
    `x+y=p_(1)+p_(2)`
    C
    `x^(2)-y^(2)=p_(1)^(2)-p_(2)^(2)`
    D
    `x-y=p_(1)-p_(2)`

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