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Question

A line through A(-5, -4) meets the line x+3y+2=0, 2x+y+4=0 and x-y-5=0 at B comma C and D respectively. If left parenthesis fraction numerator 15 over denominator A B end fraction right parenthesis to the power of 2 end exponent plus left parenthesis fraction numerator 10 over denominator A C end fraction right parenthesis to the power of 2 end exponent equals left parenthesis fraction numerator 6 over denominator A D end fraction right parenthesis to the power of 2 end exponent then the equation of the line is

  1. 2x+3y+22=0    
  2. 3x+2y+23=0    
  3. x+y+9=0    
  4. 3x+y+19=0    

The correct answer is: 3x+2y+23=0


    AB equals fraction numerator 15 over denominator vertical line blank c o s blank theta plus 3 blank s i n blank theta vertical line end fraction comma A C equals fraction numerator 10 over denominator vertical line 2 blank c o s blank theta plus blank s i n blank theta vertical line end fraction comma A D equals fraction numerator 6 over denominator blank c o s blank theta minus blank s i n blank theta end fraction
    rightwards double arrow left parenthesis blank c o s blank theta plus 3 blank s i n blank theta right parenthesis to the power of 2 end exponent plus left parenthesis 2 blank c o s blank theta plus blank s i n blank theta right parenthesis to the power of 2 end exponent equals left parenthesis blank c o s blank theta minus blank s i n blank theta right parenthesis to the power of 2 end exponent
    4 blank c o s to the power of 2 end exponent theta plus 12 blank s i n blank theta blank c o s blank theta plus 9 s i n to the power of 2 end exponent theta equals 0 blank rightwards double arrow 2 blank c o s blank theta plus 3 blank s i n blank theta equals 0
    m equals blank t a n blank theta equals fraction numerator negative 2 over denominator 3 end fraction

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