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AP EAMCET202317 May 2023Morning ShiftMathematicsStraight LinesActual

A straight line L at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and the perpendicular drawn from the origin to this line makes an angle of 60^ with the line x+y=0 . Then the equation of the line L is

Options

  1. A( 3 +1) x+( 3 -1) y=8 2
  2. B( 3 -1) x+( 3 +1) y=8 2
  3. C3 x+y=8
  4. Dx+ 3 y=8

Correct answer

B. ( 3 -1) x+( 3 +1) y=8 2

Step-by-step solution

Given: O P=4 ~cm Slope of y+x=0 is -1 . Slope of O P is . Then, 60+ =135^ =75^ Now, 75^ = (30^ +45^ )= 3 2 2 - 1 2 2 75^ = (30^ +45^ )= 3 2 2 - 1 2 2 Now, equation of line L is aligned & x +y =d x 75^ +y 75^ =4 & x ( 3 2 2 - 1 2 2 )+y ( 3 2 2 + 1 2 2 )=4 & ( 3 -1) x+( 3 +1) y=8 2 aligned

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