If the equation a x²+2 h x y+b y²+2 g x+2 f y=0 has one line as the bisector of the angle between co-ordinate axes, then

Step-by-step solution

(A) In the given pair of lines, one line is y= x x y=0 Let the other line be a x+b y+c=0 (a x+b y+c)(x+y)=0 or (a x+b y+c)(x-y)=0a x²+b x y+c x+a x y+b y²+c y=0 or a x²+b x y+c x-a x y-b y²-c y=0a x²+(a+b) x y+b y²+c x+c y=0 (1) or a x²+(b-a) x y-b y²+c x-c y=0 (2) Given eq. is a x²+2 h x y+b y²+2 g x+2 f y=0 (3) Eq. (1) and (3) as well as eq. (2) and (3) represent the same line. Comparing, we write 2 h=a+b or 2 h=b-a 4 h²=(a+b)² among options given.