Find the equation of a line perpendicular to the line `3x+y+5=0` and at a distance of 3 units from the origin.

Explanation

The line perpendicular to `sqrt(3)x -y + 5 = 0 `is `x + sqrt(3)x + lambda = 0`


It is given that the line `x + sqrt(3)x + lambda = 0 `is at a distance of 3 units from the origin.

Thus value obtained is
⇒ `lambda = ± 6`


Substituting the value of lambda, We get `x + sqrt(3)y ± 6 = 0`.
Hence, equation of the required line is `x + sqrt(3)y ± 6 = 0`