General Equation of Pair of Lines

If $\varphi$ is the acute angle between the lines given by $3x^2-4xy+b{y}^2=0$ and $\tan \varphi =\frac{1}{2}$ then $b=$

The line $y=3x$ bisects the angle between the lines $a{x}^2+2axy+y^2=0$ if $a=?$

Equation of all lines passing through the intersection of lines $2x+3y=5$ and $x+y=2$ is given by $(2x+3y-5)+\lambda (x+y-2)=0$, of all these lines one line is farthest from point $(7,4)$, the value of $\lambda$ is :

Find the distance between the parallel lines $y=mx+c$ and $y=mx+d$.

Two sides of a square lie on the lines $x+y=1$ and $x+y+2=0$. Then the area is:

Find the distance between the parallel lines $3x-4y+9=0$ and $6x-8y-15=0$. (Write the answer in fraction and in $\mathrm{units}$)

Find the product of the lengths of the perpendiculars drawn from $(2,1)$ upon the lines $12x^2+25xy+12y^2+10x+11y+2=0$.

 If the line $x+2=0$ coincides with one of the lines represented by the equation $x^2+2xy+4y+k=0,$ then find 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 $\theta$ is the acute angle between the pair of lines represented by the equation $2x^2-xy-3y^2-6x+19y-20=0$ then, $\theta =$

Find the value of $k$, if the following equation represents a pair of lines :

$x^2+3xy+2y^2+x-y+k=0$

Find the value of $k$, if the following equation represents a pair of lines :

$kxy+10x+6y+4=0$

Find the value of $k$, if the following equation represents a pair of lines :

$3x^2+10xy+3y^2+16y+k=0$

 If the line $x+2=0$ coincides with one of the lines represented by the equation $x^2+2xy+4y+k=0,$ then find 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

Find the value of $k$, if the following equation represents a pair of lines :

$x^2+3xy+2y^2+x-y+k=0$

Find the value of $k$, if the following equation represents a pair of lines :

$kxy+10x+6y+4=0$

Find the value of $k$, if the following equation represents a pair of lines :

$3x^2+10xy+3y^2+16y+k=0$

Find $k,$if one of the lines given by $3x^2-kxy+5y^2=0$is perpendicular to the line $5x+3y=0.$