If the pair of straight lines `a x^2+2h x y+b y^2=0` is rotated about the origin through `90^0` , then find the equations in the new position.

If the pair of lines sqrt(3)x^2-4x y+sqrt(3)y^2=0 is rotated about the origin by pi/6 in the anticlockwise sense, then find the equation of the pair in the new position.

A DeltaOPQ is formed by the pair of straight lines x^(2)-4xy+y^(2)=0 and the line PQ. The equation of PQ is x+y-2=0. Find the equation of the median of the triangle DeltaOPQ drawn from the origin O.

If the line joining two points A(2,0) and B(3,1) is rotated about A in anticlockwise direction through an angle of 15^(@) , then find the equation of the line in new position.

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 a line joining two points (3,0) and (5,2) is rotated about the point (3,0) in counter clockwise direction through an angle 15^@ , Then find the equation of the line in the new position.

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 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 a point A(6,8) rotates through an angle 90^o about the origin in the anticlockwise direction ,find the new position of A.