Statement-1: If −2h=a+b, then one line of the pair of lines ax2+2hxy+by2=0 bisects the angle between the coordinate axes in the positive quadrant.Statement 2: If ax+y(2h+a)=0 is a factor of ax2+2hxy+by2=0,then b+2h+a=0.

Put 2h=−(a+b) in ax2+2hxy+by2=0. Then, ax2−(a+b)xy+by2=0or (x−y)(ax−by)=0Therefore, 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)yHence, ax+(2h+a)y  is a factor of ax2+2hxy.However, statement 2 is not the correct explanation of statement 1.