If $P$ is the set of all real numbers $\alpha$ such that the product of the lengths of perpendiculars from $(\alpha, 1)$ to the pair of straight lines $3x^2+7xy+2y^2=0$ is $\frac{\sqrt{2}}{5}$,then the sum of the elements in $P$ is

If one of the lines given by the equation $2x^2 + axy + 3y^2 = 0$ coincides with one of those given by the equation $2x^2 + bxy - 3y^2 = 0$,while the other two lines are perpendicular to each other,then the values of $a$ and $b$ are

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

The area of the triangle formed by the pair of straight lines $(ax+by)^2 - 3(bx-ay)^2 = 0$ and the line $ax+by+c = 0$ is

$2 x^2-3 x y-2 y^2=0$ 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 line $\frac{x}{3}+\frac{y}{2}=1$ and a pair of lines both passing through the origin form an isosceles triangle. If this pair of lines are perpendicular,then the equation of the pair of straight lines is