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JEE Main20268 April 2026Evening ShiftMathematicsStraight LinesActual

If a straight line drawn through the point of intersection of the lines 4x+3y-1=0 and 3x+4y-1=0 , meets the co-ordinate axes at the points P and Q, then the locus of the mid point of PQ is:

Options

  1. Ax+y-7=0
  2. Bx+y-14xy=0
  3. C2x+y+14xy=0
  4. Dx+2y-14xy=0

Correct answer

B. x+y-14xy=0

Step-by-step solution

The point of intersection of the lines 4x+3y-1=0 and 3x+4y-1=0 is obtained by solving them simultaneously. Adding the two equations gives 7x+7y-2=0 x+y= 2 7 . Subtracting the two equations gives x-y=0 x=y . Thus, the point of intersection is ( 1 7 , 1 7 ) . Let the equation of the line passing through this point and meeting the coordinate axes at P and Q be x a + y b = 1 . Since the line passes through ( 1 7 , 1 7 ) , we have: 1 7a + 1 7b = 1 1 a + 1 b = 7 The coordinates of the points where the line meets the axes

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