The equation of the chord of the circle x2+y2−3x−4y−4=0 which passes through the origin such that the origin divides it in the ratio 4 : 1, is

The equation of the chord of the circle x2+y23x4y4=0 which passes through the origin such that the origin divides it in the ratio 4 : 1, is

  1. A

    x = 0

  2. B

    24x+7y=0

  3. C

    7x+24y=0

  4. D

    7x24y=0

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    Solution:

    Let y = mx be a chord.
    Then the points of intersections are given by
    x21+m2x(3+4m)4=0 x1+x2=3+4m1+m2 and x1x2=41+m2
    Since (0, 0) divides chord in the ratio 1 : 4, we have
     x2=4x1 3x1=3+4m1+m2 and 4x12=41+m29+9m2=9+16m2+24m i.e., m=0,247
    Therefore, the lines are y= 0 and 7y + 24 x = 0.
     

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