Equations of Pair of Lines

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

The slopes of the lines represented by $x^2+2hxy+2y^2=0$ are in the ratio $(1: 2)$ then $h=$

Which among the following represents the combined equation of a pair of lines through point $(1,0)$ and parallel to the lines represented by $2x^2-xy-y^2=0$.

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

Find the length of the intercept cut by the pair of lines $2x^2+4xy-4y^2-6x-8y+7=0$ over the $y$-axis.

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 equation $8x^2+8\mathrm{xy}+2{\mathrm{y}}^2+26\mathrm{x}+13\mathrm{y}+15=0$ represents a pair of parallel straight lines then the distance between them is

If the product of the perpendiculars from origin to the pairs of lines $xy+x+y+1=0,$ $x^2-y^2+2x+1=0$ and $2x^2+3xy-2y^2+2x+1=0$ respectively are $p_1, p_2, p_3,$ then

A chord through the point $(1, -2)$ cuts the curve $3{\mathrm{x}}^2-y^2-2\mathrm{x}+4\mathrm{y}=0$ at $P$ and $Q.$ If $PQ$ subtends an angle $\text{'}\theta \text{'}$ at the origin, then $\theta$ equals $\_\_\_\_\_\_\_\_\_\_$

If $4x^2-5xy+y^2=0$ represents a pair of lines with slopes $m_1$ and $m_2,$ then the value of $\left|m_1-m_2\right|$ equals ______

If slopes of lines represented by $K{x}^2+5xy+y^2=0$ differ by $\text{1}$ then $K=$

If $x^2+y^2+2gx+2fy+1=0$ represents a pair of straight lines, then $f^2+g^2$ is equal to

If lines represented by equation $p{x}^2-q{y}^2=0$ are distinct then

Find $a$, if the sum of slopes of lines represented by $a{x}^2+8xy+5y^2=0$ is twice their product.

Find $k,$ if one of the lines given by $6x^2+kxy+y^2=0$ is $2x+y=0.$

Find $k,$ if the slopes of lines given by  $k{x}^2+5xy+y^2=0$ differ by $1.$

Find $k,$ if the slope of one of the lines given by $3x^2-4xy+k{y}^2=0$ is $1.$

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 $k=$

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