Question

The bisector of two line L1 and L2 are given by 3x^2-8xy-3y^2+10x+20y-25.If the line L1 passes through the origin find L2???

Answer 1

Let line L1 be y=mx 

Let line L2 be ax+by+c=0 

Equation of bisector of angle made by the L1 and L2 will be given by 

2ac/a square + b square  

= -10 and 2bc/ a square + b square = -20 

4ac square  = (-10) whole square + (-20) whole square = 500 ===> c = plus minus 5 under root 5 

===> a/b = ½ 

C square/a square + b square = 25 ===> a square + b square   

= 5 ==> b  

= plus minus 2 and a = plus minus 1  

X+2y  +5 under root 5 = 0