Second Degree General Equation

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 :

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

If the equation $x^2+2\sqrt{2}xy+2y^2+4x+4\sqrt{2}y+1=0$ represents a pair of straight lines which are parallel to each other, find the distance between them

Find the condition that the equation $a{x}^2+b{y}^2+cx+cy=0$  may represent a pair of lines.
 

 Show that the following equations represent a pair of lines. Find the acute angle between them.

${\left(x-3\right)}^2+\left(x-3\right)\left(y-4\right)-2{\left(y-4\right)}^2=0$

Show that the following equations represent a pair of lines. Find the acute angle between them.

$2x^2+xy-y^2+x+4y-3=0$

Find $p$ and $q$, if the equation $2x^2+8xy+p{y}^2+qx+2y-15=0$  represents a pair of parallel lines.

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

Show that the following equation represents a pair of lines, find the acute angle between the pair :

$2x^2+xy-y^2+x+4y-3=0$

Show that the following equation represents a pair of lines, find the acute angle between the pair :

$2x^2-xy-3y^2-6x+19y-20=0$

Consider a pair of perpendicular straight lines $a{x}^2+3xy-2y^2-5x+5y+c=0$. The value of $c$ is:

The value of k such that $3x^2–11xy+10y^2–7x+13y+k=0$ may represent a pair of straight lines, is ________

The equation $4x^2+12xy+9y^2+2gx+2fy+c=0$ will represents two real parallel straight lines, if

If $6x^2+11xy-10y^2+x+31y+k=0$ represents a pair of straight lines, then $k$ =

If the equation $12x^2-10xy+2y^2+11x-5y+K=0$ represents two straight lines, then the value of $K$ is

The value of $k$ such that $3x^2-11xy+10y^2-7x+13y+k=0$ may represent a pair of straight lines, is

If the equations, $12x^2-10xy+2y^2+11x-5y+k=0$ represents two straight lines, then the value of $k$ is