The number of possible distinct straight lines passing through $(2,3)$ and forming a triangle with co-ordinate axes whose area is 12 sq . units are,

The line L given by $\frac{x}{5}+\frac{y}{b}=1$ passes through the point $(13,32)$. The line K is parallel to L and has the equation $\frac{x}{c}+\frac{y}{3}=1$. Then the distance between $L$ and $K$ is

The diagonals of a parallelogram $A B C D$ are along the lines $x+3 y=4$ and $6 x-2 y=7$. Then ABCD must be a

If the equation $7 x^2-14 x y+p y^2-12 x+q y-4=0$ represents a pair of parallel lines then the value of $\sqrt{p^2+q^2-p q}$ is