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JEE Main2014MathematicsStraight LinesActual

If the three distinct lines x+2 a y+a=0, x+3 b y+b=0 and x+4 a y+a=0 are concurrent, then the point (a, b) lies on a :

Options

  1. Acircle
  2. Bhyperbola
  3. Cstraight line
  4. Dparabola

Correct answer

C. straight line

Step-by-step solution

aligned &x+2 a y+a=0 &x+3 b y+b=0 &x+4 a y+a=0 aligned Subtracting equation (3) from (1) aligned &-2 a y=0 &a y=0 y=0 aligned Putting value of y in equation (1), we get aligned &x+0+a=0 &x=-a aligned Putting value of x and y in equation (2), we get aligned &-a+b=0 &a=b aligned Thus, (a, b) lies on a straight line

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