Find the equation of the bisectors of the angle between the lines represented by 3x2−5xy+4y2=0
5x2−2xy−5y2=0
Given equation is
3x2−5xy+4y2=0
Comparing this equation of with standard pair of straight lines passing through origin ax2+2hxy+by2=0
We have a = 3, b = 4, h=−52
Now the equation of the bisector of the angle between the pair of lines (1)
x2−y2a−b=xyh
Substituting the value of a,b and h
x2−y23−4=xy−52;
x2−y2−1=2xy−5or5x2−5y2=2xy
5x2−2xy−5y2=0