If the area of the triangle formed by the pair of lines $8x^2-6xy+y^2=0$ and the line $2x+3y=a$ is $7$,then $a$ is equal to

$2 x^2-3 x y-2 y^2=0$ represents two lines $L_1$ and $L_2$. $2 x^2-3 x y-2 y^2-x+7 y-3=0$ represents another two lines $L_3$ and $L_4$. Let $A$ be the point of intersection of lines $L_1$ and $L_3$,and $B$ be the point of intersection of lines $L_2$ and $L_4$. The area of the triangle formed by lines $AB$,$L_3$,and $L_4$ is

The pairs of straight lines $x^2-3xy+2y^2=0$ and $x^2-3xy+2y^2+x-2=0$ form a

If the angle between the pair of lines $x^2+2 \sqrt{2} x y+k y^2=0, k>0$ is $45^{\circ}$,then the area (in square units) of the triangle formed by the pair of bisectors of angles between the given lines and the line $x+2 y+1=0$ is

If the equations $3x^2 + 2hxy - 3y^2 = 0$ and $3x^2 + 2hxy - 3y^2 + 2x - 4y + c = 0$ represent the four sides of a square,then $\frac{h}{c} =$

The area of the region enclosed between the pair of lines $xy = 0$ and the lines $xy + 5x - 4y - 20 = 0$ is .....