The correct option (c) 5x + 5y – 3 = 0
Explanation:
line x + 3y – 2 = 0 bisects angle between lines x – 7y + 5 = 0 and other line. point of intersection of two lines:
x + 3y – 2 = 0 & x – 7y + 5 = 0
∴ y = (7/10) & x = [(– 1)/10]
∴ (x, y) = [{(– 1)/10}, (7/10)] ......(1)
Let new line has slope m. The angle between bisector and new line will be same as between bisector and line x – 7y + 5 = 0
∴ [{(1/7) + (1/3)}/{1 – (1/21)}] = [{m + (1/3)}/{1 – (m/3)}]
∴ (10/20) = [(3m + 1)/(3 – m)] ⇒ m = – 1 or m = (1/7)
∴ m = – 1 ....(2)
∴ from (1) & (2), equation of line is [y – (7/10)] = (– 1)[x + (1/10)]
i.e. 5x + 5y = 3
