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AP EAMCET202315 May 2023Morning ShiftMathematicsStraight LinesActual

The combined equation of the lines passing through the point (3,4) and each making an angle 45^ with the line x+y+1=0 is

Options

  1. Ax y-4 x-3 y+12=0
  2. B(3 x -2 y -1)( x -2 y +2)=0
  3. C(3 x+2 y-17)(x+2 y-11)=0
  4. Dx y-4 x+3 y+12=0

Correct answer

A. x y-4 x-3 y+12=0

Step-by-step solution

All the lines passing from pt (3,4) is (y-4)=m(x-3) where m= slope Slope of given line x+y+1=0 is 3 4 Hence m₁= 3 4 + 4 = and m₂= 3 4 - 4 = 2 will be the slopes of lines which make 4 angle with x+y+1=0 When m=m₁= then equation of line is y-4=0(x-3) (y-4)=0 When m=m₂= 2 then equation of line is y-4= 1 0 (x-3) (x-3)=0 Hence combined equation is (x-3)(y-4)=0 x y-4 x-3 y+12=0

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