lines `L_1:ax+by+c=0` and `L_2:lx+my+n=0` intersect at the point `P` and make a angle `theta` between each other. find the equation of a line `L`different from `L_2` which passes through `P` and makes the same angle `theta` with `L_1`

Explanation

Since, the required line l passes through intersection of `L1=0` and `L2=0`

So, the equation of the required line L is

`L1+lambdaL2=0`

`=>(ax+by+c)+lambda(lx+my+n)=0 ...(1)`


Since, `L1` is the angle bisector of `L=0` and `L2=0`

So,

`=>(∣lx_1+my_1+n∣)/(sqrt(1^2+m2))`

...