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AP EAMCET202021 Sep 2020Morning ShiftMathematicsStraight LinesActual

The equation of the line through the intersection of (3 x-4 y+1 ) and (5 x+y-1=0 ) which cuts off equal intercepts on the axes is given by

Options

  1. A(23 x+23 y-11=0 )
  2. B(23 x+23 y+11=0 )
  3. C(23 x-23 y-11=0 )
  4. D(23 x-23 y+11=0 )

Correct answer

A. (23 x+23 y-11=0 )

Step-by-step solution

Equation of family of lines passes through the intersection of lines (3 x-4 y+1=0 ) and (5 x+y-1=0 ) is ( aligned & (3 x-4 y+1)+ (5 x+y-1) =0 & (3+5 ) x+( -4) y+(1- ) =0 & x -1 5 +3 + y -1 =1, 1 aligned ) ( ) The obtain lines makes equal intercepts with the axes, so ( aligned & | -1 5 +3 | = | -1 -4 | & | -4| =|5 +3| 1 & =- 7 4 , 1 6 aligned ) ( ) Equation of required lines are (-23 x-23 y+11=0 ) and (23 x-23 y+5=0 ) or (23 x+23 y-11=0 ) and (23 x-23 y+5=0 ) Hence, option (a) is correct.

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