Correct Answer - 2
Put `2h=-(a+b)`in`ax^(2)+2hxy+by^(2)=0`. Then ,
`ax^(2)-(a+b)xy+by^(2)=0`
or `(x-y)(ax-by)=0`
Therefore , one of the lines bisects the angle between the coordinates axes in the positive quadrant. Also , putting
`b=-2h-a` in `ax-by` ,we have
`ax-by=ax-(-2h-a)y=ax+(2h+a)y`
Hence , `ax+(2h+a)y` is a factor of `ax^(2)+2hxy+by^(2)` . However, statement 2 is not the correct explanation of statement 1.