Pair of Straight Lines

If sum of slopes of lines $kx^{2}-10xy-9y^{2}=0$ is five times their product, then $k=$

The equation of the lines passing through the origin and having slopes 3 and $-\dfrac{1}{3}$, is

The pair of straight lines represented by the equation $\sqrt{3} x^{2}-4 x y+\sqrt{3} y^{2}=0$ are

The joint equation of the bisector of the angle between the lines $2 x^{2}+11 x y+3 y^{2}=0$ is

The circumcenter of the triangle formed by lines $x y+2 x+2 y+4=0$ and $x+y+2=0$ is

If the pair of straight lines $x y-x+y-1=0$ and the line $x+\mathrm{k} y-3=0$ are concurrent, then the value of $k$ is equal to

The circumradius of the triangle formed by the lines $x y+2 x+2 y+4=0$ and $x+y+2=0$ is

The slopes of the lines represented by $6 x^{2}+2 \mathrm{hxy}+y^{2}=0$ are in the ratio 2 : 3, then $\mathrm{h}=$

If one of the lines represented by $a x^{2}+2 h x y+b y^{2}=0$ is perpendicular to $\mathrm{m} x+\mathrm{n} y=18$ ，then

The equation $x^{2}-3 x y+2 y^{2}+3 x-5 y+2=0$ represents a pair of straight lines. If $\theta$ is the angle between them, then the value of $\cos \theta$ is equal to

The joint equation of pair of lines through the origin, each of which makes an angle of 30° with Y -axis, is

If one of the lines $2x^{2}-xy-15y^{2}=0$ is perpendicular to the line $kx+y=0$, then $k=$

If the distance between the lines represented by $(x-2 y)^{2}+k(x-2 y)=0$ is 3 units and $k > 0$ then the equations of the lines are

If the equation $k x^{2}-5 x y+6 y^{2}+x-3 y=0$ represents a pair of straight lines, then the co-ordinates of their point of intersection are

The joint equation of two lines through the origin, each making an angle with measure of 30° with the positive Y -axis, is