The equation $xy + a^2 = a(x + y)$ represents

The equation $4x^2 - 24xy + 11y^2 = 0$ represents

If the lines represented by the equation $6x^2 + 41xy - 7y^2 = 0$ make angles $\alpha$ and $\beta$ with the $x$-axis,then $\tan \alpha \cdot \tan \beta = $

If the sum of the slopes of the pair of lines represented by $4x^2 + 2hxy - 7y^2 = 0$ is equal to the product of the slopes,then the value of $h$ is

If the slope of one line is twice the slope of the other in the pair of straight lines $ax^2+2hxy+by^2=0$,then $8h^2$ is equal to (in $ab$)

The equation of the perpendiculars drawn from the origin to the lines represented by the equation $2x^2 - 10xy + 12y^2 + 5x - 16y - 3 = 0$ is