Find the joint equation of pair of lines through the origin and perpendicular to the lines given by $x^2+4xy-5y^2=0$

Find $k$ if

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

Find $k$ if

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

Find the joint equation of a pair of lines which bisects angle between the lines given by $x^2+3xy+2y^2=0$

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

$9x^2-6xy+y^2+18x-6y+8=0$