The combined equation of a pair of lines passing through the origin and inclined at $$60^{\circ}$$ and $$30=$$ respectively with $$x$$-axis is

If the sum of slopes of lines represented by $$\mathrm{ax^2+8xy+5y^2=0}$$ is twice their product, then a =

If the line joining two points $$\mathrm{A}(2,0)$$ and $$\mathrm{B}(3,1)$$ is rotated about $$\mathrm{A}$$ in anticlockwise direction through an angle of $$15^{\circ}$$, then the equation of the line in new position is

If lines represented by the equation $$\mathrm{px}^2-\mathrm{qy^{2 }}=0$$ are distinct, then