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AP EAMCET2012MathematicsStraight Lines

The equation of a straight line passing through the point (1,2) and inclined at 45^ to the line y=2 x+1 is

Options

  1. A5 x+y=7
  2. B3 x+y=5
  3. Cx+y=3
  4. Dx-y+1=0

Correct answer

B. 3 x+y=5

Step-by-step solution

Let required equation of line is y=m x+c Since, angle between y=m x+c and y=2 x+1 is 45^ array ll = | m₁-m₂ 1+m₁ m₂ | & 45^ = | m-2 1+2 m | & 1= m-2 1+2 m & 1+2 m=m-2 or & 1+2 m=-m+2 & m=-3 or 3 m=1 & m=-3 or 1 3 array On putting m=-3 in Eq. (i), we get y=-3 x+c Since, it passes through (1,2) . aligned & 2=-3+c & c=5 & y=-3 x+5 & 3 x+y=5 & aligned Again, putting m= 1 3 in Eq. (i), we get y=- x 3 +c Since, it passes through (1,2) . 2=- 1 3 +c c= 7 6 Equation of line is y=- x 3 + 7 6 6 y+2 x=7 Hence, option (b) is co

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