If one of the lines denoted by the line pair `a x^2+2h x y+b y^2=0` bisects the angle between the coordinate axes, then prove that `(a+b)^2=4h^2`

If one of the lines of the pair a x^2+2h x y+b y^2=0 bisects the angle between the positive direction of the axes. Then find the relation for a ,b and h .

If one of the pair of lines ax^2+2hxy+by^2=0 bisects the angle between coordinate axes in positive quadrant, then

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 .

If one of the pair of lines ax^2+2hxy+by^2=0 bisects the angle between positive directions of the axes, a, b, h satisfy the relation

If the pair of lines a x^2+2h x y+b y^2+2gx+2fy+c=0 intersect on the y-axis, then prove that 2fgh=bg^2+c h^2

The lines y = mx bisects the angle between the lines ax^(2) +2hxy +by^(2) = 0 if

Prove that two of the four lines represented by the joint equation ax^4+bx^3y+cx^2y^2+dxy^3+ay^4=0 will bisect the angles between the other two if c+6a=0 and b+d=0

The line y=sqrt(3)x bisects the angle between the lines ax^(2)+2axy+y^(2)=0 if a is equal to

The condition that one of the straight lines given by the equation a x^2+2h x y+b y^2=0 may coincide with one of those given by the equation a^(prime)x^2+2h^(prime)x y+b^(prime)y^2=0 is (a b^(prime)-a^(prime)b)^2=4(h a^(prime)-h^(prime)a)(b h^(prime)-b^(prime)h) (a b^(prime)-a^(prime)b)^2=(h a^(prime)-h^(prime)a)(b h^(prime)-b^(prime)h) (h a^(prime)-h^(prime)a)^2=4(a b^(prime)-a^(prime)b)(b h^(prime)-b^(prime)h) (b h^(prime)-b^(prime)h)^2=4(a b^(prime)-a^(prime)b)(h a^(prime)-h^(prime)a)

Find the angle between the lines represented by x^2+2x ysectheta+y^2=0