If `x^2-2p x y-y^2=0` and `x^2-2q x y-y^2=0` bisect angles between each other, then find the condition.

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 of lines represented by x^2-2cxy-y^2= 0 and x^2-2dxy-y^2=0 be such that each pair bisects the angle between the other pair, prove that cd = -1.

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 pairs of lines x^2+2x y+a y^2=0 and a x^2+2x y+y^2=0 have exactly one line in common, then the joint equation of the other two lines is given by (a) 3x^2+8x y-3y^2=0 (b) 3x^2+10 x y+3y^2=0 (c) y^2+2x y-3x^2=0 (d) x^2+2x y-3y^2=0

If two lines represented by x^4+x^3y+c x^2y^2-x y^3+y^4=0 bisect the angle between the other two, then the value of c is (a) 0 (b) -1 (c) 1 (d) -6

If two lines represented by x^4+x^3y+c x^2y^2-x y^3+y^4=0 bisect the angle between the other two, then the value of c is (a) 0 (b) -1 (c) 1 (d) -6

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

If the circles x^2+y^2+2a x+c y+a=0 and x^2+y^2-3a x+d y-1=0 intersects at points P and Q , then find the values of a for which the line 5x+b y-a=0 passes through Pa n dQdot