The line 'x + 3y - 2 = 0' bisects the angle between a pair of straight lines of which one has equation 'x - 7y + 5 = 0' , then find equation of other line.

Options

A. 3x+3y-1=0
B. x-3y+2=0
C. 5x+5y-3=0
D. none of these

Answer

C

Explanation

The family of line through the given lines is
`L-=x-7y+5+lambda(x+3y-2)=0 " " (1)`
For line L=0 in the diagram, the distance of any point say (2,0) on the line x+3y-2=0 from the line x-7y+5=0 and the line L=0 must be the same. Therefore,
`|(2+5)/(sqrt(50))| = |(2+2lambda+5-2lambda)/(sqrt((1+lambda)^(2) + (3lambda-7)^(2)))|`
`"or " 10lambda^(2)-40lambda = 0`
`"i.e., " lambda = 4 or 0`
`"Hence, "L=0, lambda = 4`
Therefore, the required line is 5x+5y-3=0.