A is the point of intersection of the lines 3 x+y-4=0 and x-y=0 . If a line having negative slope makes an angle of 45^ with the line x-3 y+5=0 and passes through A then its equation is

Step-by-step solution

Since, intersection point of the lines 3 x+y-4=0x-y=0 is A (1,1) Now, slope of line x-3 y+5=0 is 1 3 and slope of required line (m) = | 45^ - 1 3 1+ 45^ 3 |= | 1- 1 3 1+ 1 3 |= -2 4 = -1 2 So, equation of required line is y-1= -1 2 (x-1) y= -x 2 + 1 2 +1 2 y+x=3