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The equation of the locus of the middle ...

The equation of the locus of the middle point of a chord of the circle `x^2+y^2=2(x+y)` such that the pair of lines joining the origin to the point of intersection of the chord and the circle are equally inclined to the x-axis is (a) `x+y=2` (b) `x-y=2` (c) `2x-y=1` (d) none of these

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Knowledge Check

  • The locus of the midpoints of chords of the circle x^(2) + y^(2) = 1 which subtends a right angle at the origin is

    A
    `x^(2) +y^(2) =(1)/(4)`
    B
    `x^(2) + y^(2) = (1)/(2)`
    C
    `xy = 0 `
    D
    `x^(2) - u^(2) = 0 `

  • The locus of the mid-points of the chords of the circle x^(2)+y^(2)+2x-2y-2=0 which make an angle of 90^(@) at the centre is

    A
    `x^(2)+y^(2)+2x-2y-2=0`
    B
    `x^(2)+y^(2)-2x+2y=0`
    C
    `x^(2)+y^(2)+2x-2y=0`
    D
    `x^(2)+y^(2)+2x-2y-1=0`

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    The angle between the lines joining the origin to the points of intersection of the line sqrt3x+y=2 and the curve y^(2)-x^(2)=4 is

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