If equation $a{x}^2-y^2+2y+c=1$ represents a pair of perpendicular lines then find $a$ and $c$

Find the combined equation of the following pairs of lines:

$2x+y=0$ and $3x-y=0$

Find the combined equation of the following pairs of lines:

$x+2y-1=0$ and $x-3y+2=0$

Find the joint equation of the pair of lines:

Passing through $\left(2,3\right)$ and parallel to the co-ordinate axes.

Find the joint equation of the following pair of lines:

Passing through $\left(2,3\right)$ and perpendicular to the lines $3x+2y-1=0$ and $x-3y+2=0$

Find the joint equation of the following pair of lines:

Passing through $\left(-1,2\right)$, one is parallel to $x+3y-1=0$ and other is perpendicular to $2x-3y-1=0.$

Find the separate equations of the lines represented by the following equation:

$3y^2+7xy=0$

Find the separate equations of the lines represented by the following equation:

$5x^2-9y^2=0$

Find the separate equations of the lines represented by the following equations:

$x^2-4xy=0$