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.

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.

If the pair of straight lines xy - x - y +1=0 & the line ax+2y-3=0 are concurrent then a =

A line through the point P (1, 2) makes an angle of 60^0 with the positive direction of x-axis and is rotated about P in the clockwise direction through an angle 15^0 . Find the equation of the straight line in the new position.

If the lines represented by x^(2)-2pxy-y^(2)=0 are rotated about the origin through an angle theta , one clockwise direction and other in anti-clockwise direction, then the equation of the bisectors of the angle between the lines in the new position is

A line through the point A(2, 0) which makes an angle of 30^0 with the positive direction of x-axis is rotated about A in clockwise direction through an angle 15^0 . Find the equation of the straight line in the 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 and h .

Show that the pairs of straight lines 2x^2+6x y+y^2=0 and 4x^2+18 x y+y^2=0 are equally inclined,then b is equal to

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