Prove that one of the straight lines given by `ax^(2)+2hxy+by^(2)=0` will bisect the angle between the co-ordinate axes if `(a+b)^(2)=4h^(2)`.

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.

If h^(2)=ab then the angle between the pair of straight lines given by ax^(2)+2hxy+by^(2)=0 is

The slope of one of the straight lines ax^(2)+2hxy+by^(2)=0 is three times the other, show that 3h^(2)=4ab .

The slope of one of the straight lines ax^(2)+2hxy+by^(2)=0 is twice that of the other, show that 8h^(2)=9ab .

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

The condition that the pair of straight lines ax^(2)+2xy+by^(2)=0 are parallel is:

If h^(2)=ab then the angle between the pair of straight lines given by ax^2+2hxy+by^2=0 is

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 ,h

If the pair of straight lines ax^(2)-2pxy-y^(2)=0and x^(2)-2qxy-y^(2)=0 are such that each pair bisects the angle between the other pair , then prove that pq=-1 .

If the pairs of straight lines x^(2) - 2pxy-y^(2)=0 and x^(2) – 2qxy - y^(2) = 0 be such that each pair bisects the angle between the other pair, then