If the pair of lines represented by $3x^2 - 5xy + Py^2 = 0$ and $6x^2 - xy - 5y^2 = 0$ have one line in common,then the sum of all possible values of $P$ is

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):

The triangle formed by the lines $2x^2 - 3xy - 2y^2 = 0$ and $3x - y = 7$ is...

The area of the triangle formed by the lines $y^2 - 9xy + 18x^2 = 0$ and $y = 9$ 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 $a + b + c =$

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