If pairs of straight lines $x^2-2 p x y-y^2=0$ and $x^2-2 q x y-y^2=0$ are such that each pair bisects the angle between the other pair,then:

If the equation $3x^2+7xy+2y^2+2gx+2fy+2=0$ represents a pair of intersecting lines and the square of the distance of their point of intersection from the origin is $\frac{2}{5}$,then $f^2+g^2=$

If the lines represented by $x^2-2hxy-y^2=0$ are rotated about $(0,0)$ through an angle $\alpha$,one in the clockwise direction and the other in the counter-clockwise direction,then the combined equation of the bisectors of the angle between the lines thus obtained is

The combined equation of the two lines $ax+by+c=0$ and $a'x+b'y+c'=0$ can be written as $(ax+by+c)(a'x+b'y+c')=0$. The equation of the angle bisectors of the lines represented by the equation $2x^2+xy-3y^2=0$ is:

If $ax^2+2hxy-2ay^2+3x+15y-9=0$ represents a pair of lines intersecting at $(1,1)$,then $ah=$

If the lines represented by $x^2 - 2pxy - y^2 = 0$ are rotated about the origin by an angle $\theta$ in clockwise and counter-clockwise directions respectively,then the equation of the bisector of the angle between the lines in the new position is: