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AP EAMCET202125 Aug 2021Evening ShiftMathematicsStraight LinesActual

A person standing at the junction (crossing) of 2 straight paths represented by the equations 2x − 3y + 4 = 0 and 3x + 4 y − 5 = 0, wants to reach the path whose equation is 6 x − 7 y + 8 = 0 in the least time, then the equation of the path he should follow is

Options

  1. A119x − 102 y − 125 = 0
  2. B119x + 102 y − 125 = 0
  3. C102 x + 119y − 125 = 0
  4. D102 x − 119y + 125 = 0

Correct answer

B. 119x + 102 y − 125 = 0

Step-by-step solution

Given, a person is standing at the junction of the lines, 2x − 3y + 4 = 0 … (i) 3x + 4y − 5 = 0 … (ii) Solution of Eqs. (i) and (ii) will be the junction point, where the man is standing. On solving Eqs. (i) and (ii), x= -1 17 and y= 22 17 Junction point A= ( -1 17 , 22 17 ) Given, equation of path, 6x − 7y + 8 = 0 … (iii) The person can reach this path in the least time, if he walks along the perpendicular line to Eq. (iii) aligned & from ( -1 17 , 22 17 ) . & Slope of line (iii) = - Coefficient of x Coefficient o

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