If $2x^2+3xy-2y^2=0$ represents two sides of a parallelogram and $3x+y+1=0$ is one of its diagonals,then the other diagonal is

If $(a, b)$ is the centroid of the triangle formed by the lines $4x^2 - 17xy + 4y^2 = 0$ and $x + y - 5 = 0$,and $c$ is the numerical value of the area of the triangle,then $a + b + c =$

If the slope of one of the lines represented by $a x^2+2 h x y+b y^2=0$ is the square of the other,then $\frac{a+b}{h}+\frac{8 h^2}{a b}$ is

The equations $x-y=4$ and $x^2+4xy+y^2=0$ represent the sides of a/an

If the line $2x + by + 5 = 0$ forms an equilateral triangle with the pair of lines $ax^2 - 96bxy + ky^2 = 0$,then $a + 3k =$

From the point $(3,-4)$,perpendicular lines $L_1$ and $L_2$ are drawn to each of the lines represented by $S \equiv 2x^2+3xy-2y^2-7x+y+3=0$. The area of the quadrilateral formed by the pair of lines $S=0$,$L_1$,and $L_2$ is (in square units):