This equation is generally written as aX2+2hXY+bY2=0 __(i)

Now we know that a line through origin is y=mx, let two represented by (i) be
y=m1x and
y=m2x
then
aX2+2hXY+bY2=b(y-m1)(y=m2x)
this gives
m1+m2=-2h/b and m1.m2=a/b

Also angle between (ii) is @ then
tan@=m1~m2/1+m1.m2
tan@=(h2-ab)1/2/(a+b)