Second Degree General Equation

The equation $x^2-y^2+ax+b=0$ represents a pair of lines for the ordered pair $\left(a,b\right)=$

Which of the following equation does not represent a pair of lines?

A value of $\lambda$ for which the equation $x^2-\lambda xy+2y^2+3x-5y+2=0$ may represent a pair of straight lines is

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

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

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

For what value of ${}^{\text{'}}p^{\text{'}}, y^2+xy+p{x}^2-x-2y+p=0$ represent $2$ straight lines :

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.