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AP EAMCET202422 May 2024Evening ShiftMathematicsStraight LinesActual

A line L passing through the point P (-5,-4) cuts the line x-y-5=0 and x+3 y+2=0 respectively at Q and R such that 18 P Q + 15 P R =2 , then slope of the line L is

Options

  1. A1
  2. B1 3
  3. C3
  4. D2 3

Correct answer

C. 3

Step-by-step solution

Equation of line passing through P (-5,-4) and making angle with x -axis is x+5 = y+4 =r x=-5+r , y=-4+r Equation of line PQ where Q lies on x-y-5=0 is -5+P Q +4-P Q -5=0 6 PQ = - ...(i) Equation of line PR where R lies on x+3 y+2=0 is -5+P R -12+3 P R +2=0 15 P R = +3 Given condition is 18 P Q + 15 P R =2 Using (i) and (ii) aligned & 3 -3 + +3 =2 & 4 =2 = 1 2 =2 n 3 aligned So, slope of the line is = (2 n 3 )= 3

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