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

Options

A. Both the statements are true but statement 2 is the correct explanation of statement 1.
B. Both the statements are true but statement 2 is not the correct explanation of statement 1.
C. Statement 1 is true and statement 2 is false.
D. Statement 1 is false and statement 2 is true.

Answer

2

Explanation

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.