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Let L1 be a straight line passing throu...

Let `L_1` be a straight line passing through the origin and ` L_2` be the straight line `x + y = 1` if the intercepts made by the circle `x^2 + y^2-x+ 3y = 0` on `L_1` and `L_2` are equal, then which of the following equations can represent `L_1`?

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The correct Answer is:
`x - y = 0; x + 7y = 0`
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Knowledge Check

  • In xy-plane, a straight line L_1 bisects the 1st quadrant and another straight line L_2 trisects the 2nd quadrant being closer to the axis of y . The acute angle between L_1 and L_2 is

    A
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  • A line L passes through the point P(5,-6,7) and is parallel to the planes x+y+z=1 and 2x-y-2z=3 .What is the equation of the line L ?

    A
    `(x-5)/(-1)=(y+6)/4=(z+7)/(-3)`
    B
    `(x+5)/(-1)=(y-6)/4=(z+7)/(-3)`
    C
    `(x-5)/(-1)=(y+6)/(-4)=(z+7)/3`
    D
    `(x-5)/(-1)=(y+6)/(-4)=(z-7)/(-3)`

  • Let L_(1) and L_(2) be the foollowing straight lines. L_(1): (x-1)/(1)=(y)/(-1)=(z-1)/(3) and L_(2): (x-1)/(-3)=(y)/(-1)=(z-1)/(1) Suppose the striight line L:(x-alpha)/(l)=(y-m)/(m)=(z-gamma)/(-2) lies in the plane containing L_(1) and L_(2) and passes throug the point of intersection of L_(1) and L_(2) if the L bisects the acute angle between the lines L_(1) and L_(2) , then which of the following statements is /are TRUE ?

    A
    `alpha- gamma=3`
    B
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    C
    `alpha-gamma=1`
    D
    `l+m=0`

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