Find the Equations of the straight line with the help of the given information. Suppose two straight lines **3x+4y=5** & **4x-3y=15** cut each other at the point **A**. Take 2 points **B** & **C** on those 2 lines, such that **AB=AC**. If line **BC** passes through the point **(1,2)** , then find the possible equations of the straight line **BC**. The given equations are **perpendicular** to each other & given that **AB=AC**. But I am unable to use the given information to find the solution. Please help **Thank you**

I guess you mean AB=AC instead AB=BC

1) It is not difficult to check that line _ax+by+c=0_ is ortogonal to vector _(a,b)_.

2) Target lines are parallel to one of the two bisectrix of the given lines intersection angle.

3) Since we have _3x+4y=5_ & _4x-3y=15_ equations, then _n 1=(3,4)_ and _n 2=(4,-3)_ \- ortogonal vectors with same length 5. So one of the bisectrix vector equal _n1+n2 = (7,1)_ , second is ortogonal to this (-1,7).

4) So answer is two family of lines: _7x+y+c=0_ and _-x+7y+c=0_