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MHT CET202619 April 2026Evening ShiftMathematicsStraight LinesActual

The family of straight lines 4ax + 3by + c = 0 such that a + b + c = 0 (where a, b, c are real constants) are concurrent at the point...

Options

  1. A(4, 3)
  2. B( 1 2 , 1 3 )
  3. C( 1 4 , 1 3 )
  4. D( 1 3 , 1 2 )

Correct answer

C. ( 1 4 , 1 3 )

Step-by-step solution

Given the family of straight lines 4ax + 3by + c = 0 and the condition a + b + c = 0 . Substituting c = -(a + b) into the equation of the line: 4ax + 3by - (a + b) = 0 a(4x - 1) + b(3y - 1) = 0 For the lines to be concurrent for all values of a and b , the coefficients of a and b must be zero. 4x - 1 = 0 x = 1 4 3y - 1 = 0 y = 1 3 The point of concurrency is ( 1 4 , 1 3 ) . Answer: ( 1 4 , 1 3 )

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