The straight line `y = x - 2` rotates about a point where it cuts x-axis and become perpendicular on the straight line `ax + by + c = 0` then its equation is

Options

A. `ax +by +20 = 0`
B. `ax - by - 2a = 0`
C. `bx +ay - 2b = 0`
D. `ay - bx +2b = 0`

Answer

D

Explanation

Slopes of the line in the new position is bla, since it is perpendicular to the line `ax +by +c = 0` and it cuts the x-axis . Hence the required line passes through (2,0) and its slope is bla. The required is `y - 0 = (b)/(a) (x-2)` or `ay = bx - 2b`