Pair of Straight Lines

If the lines $x^2+2xy-35y^2-4x+44y-12=0$ and $5x+\lambda y-8=0$ are concurrent then $\lambda$ equals

If a pair of lines drawn through the origin forms an isosceles right-angled triangle with the line $2x+3y=6$, then those lines are

If the lines $x^2+kxy+y^2=0$ and $x+y=1$ make up the sides of an equilateral triangle, then the value of $k^2$ equals

The distance between pair of parallel lines represented by $x^2+2xy+y^2-8ax-8ay-9a^2=0$ is _____ units

If $h^2=ab,$ then the slopes of lines represented by $a{x}^2-2hxy+b{y}^2=0$ would be in the ratio $\_\_\_\_\_\_\_\_\_$

If one line of the pair of lines $a{x}^2+2hxy+b{y}^2=0$ bisects the angle between the coordinate axis then

If the equation $2x^2+8xy+p{y}^2+qx+2y-15=0$  represents a pair of parallel lines, then

If $\theta$ is the acute angle between the pair of lines represented by the equation $2x^2-xy-3y^2-6x+19y-20=0$ then, $\theta =$

If sum of the slopes of the lines represented by $b{x}^2+kxy-3y^2=0$ is twice their product, then the value of $k=$

If the equation $2x^2+8xy+p{y}^2+qx+2y-15=0$  represents a pair of parallel lines, then

If the equation $p{x}^2-8xy+3y^2+14x+2y+q=0$  represents a pair of perpendicular lines, then

The equation of lines joining origin and points of intersection of curves ${\mathrm{x}}^2+{\mathrm{y}}^2+2\mathrm{x}\mathrm{y}=1$ and $3{\mathrm{x}}^2+5{\mathrm{y}}^2–\mathrm{ }\mathrm{x}\mathrm{y}=11$ is

The equation of lines joining origin and points of intersection of curves ${\mathrm{x}}^2+{\mathrm{y}}^2+2\mathrm{x}\mathrm{y}=1$ and $3{\mathrm{x}}^2+5{\mathrm{y}}^2–\mathrm{ }\mathrm{x}\mathrm{y}=11$ is

The angle between the lines represented by $3x^2+4xy-3y^2=0$ is

If the equation $a{x}^2+b{y}^2+cx+cy=0,c\ne 0$ represents a pair of lines, then

If the angle between the lines given by the equation $x^2-3xy+\lambda y^2+3x-5y+2=0, \lambda \ge 0,$ is ${\tan }^{-1}\left(\frac{1}{3}\right),$ then $\lambda =$

If the equation $kxy+5x+3y+2=0$ represents a pair of lines, then $k=$

If $2x^2+3xy-2y^2=0$ represents two sides of a parallelogram and $3x+y+1=0$ is one of its diagonals, then the other diagonal is

If the line $x+2y=k$, intersects the curve $x^2-xy+y^2+3x+3y-2=0$ at two points $A$ and $B$ and if $O$ is the origin, then the condition for $AOB=90°$ is

The lines represented by the equations $23x^2-48xy+3y^2=0$ and $2x+3y+4=0$ form