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 given by the equation ax^(2)+6xy+by^(2)=0 bisects the angle between the co-ordinate axes, then value of (a+b) can be :

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 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 ,a n dhdot

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

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

Statement 1 : If -h2=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 Both the statements are true but statement 2 is the correct explanation of statement 1. Both the statements are true but statement 2 is not the correct explanation of statement 1. Statement 1 is true and statement 2 is false. Statement 1 is false and statement 2 is true.

If one of the lines of ax^(2)+2hxy+by^(2)=0 bisects the angle between the axes, in the first quadrant, then

If the slope of one of the pairs of lines represented by equation a^(3) x^(2) + 2hxy + b^(3) y^(2) = 0 is square of the other, then prove that ab(a+ b) = - 2h.

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

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