Show that the pairs of straight lines `2x^2+6x y+y^2=0` and `4x^2+18 x y+y^2=0` have the same set of angular bisector.

Explanation

The equation of the first pair of lines is
`2x^(2)+6xy+y^(2)=0`
The equation of the pair of bisectors is
`3(x^(2)-y^(2))=(2-1)xy`
or `3(x^(2)-y^(2))=xy` (1) The equation of the second pair of lines is `4x^(2)+18xy+y^(2)=0`.
The equation of the pair of bisectors is `9(x^(2)-y^(2))=(4-1)xy`
`9(x^(2)-y^(2))=3xy`
or `3(x^(2)-y^(2))=xy` (2)
Equations (1) and (2) are the same.
The given pairs have same angular bisectors.