If the equation $ax^{2} + hxy + by^{2} = 0$ represents a pair of coincident lines,then

If the lines represented by the equation $4xy + 6x - 8y + c = 0$ form a rectangle with the coordinate axes,then the area of the rectangle (in sq. units) is

The combined equation of two lines $L$ and $L_1$ is $2x^2+axy+3y^2=0$ and the combined equation of two lines $L$ and $L_2$ is $2x^2+bxy-3y^2=0$. If $L_1$ and $L_2$ are perpendicular,then $a^2+b^2=$

The joint equation of two lines passing through the origin,each making an angle of $30^{\circ}$ with the positive $Y$-axis,is

If the slope of one line of the pair of lines represented by $ax^2 + 4xy + y^2 = 0$ is $3$ times the slope of the other line,then $a$ is

If two sides of a triangle are represented by $x^2 - 7xy + 6y^2 = 0$ and the centroid is $(1, 0)$,then the equation of the third side is