Let $L_1, L_2$ be the lines represented by the equation $4 x^2-5 x y+3 y^2=0$. Let $L_3, L_4$ be two lines passing through the point $(4,3)$ such that $L_3$ and $L_4$ are perpendicular to $L_1$ and $L_2$ respectively. If the combined equation of $L_3$ and $L_4$ is $a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$, and $a f+b g+c h=$

The equation $x^2-y^2+a x+b=0$ represents a pair of lines for the ordered pair $(a, b)=$

Let $A=(2,3), B=(3,-5)$ be two vertices of $\triangle A B C$ such that $C$ is a point on the line $L \equiv 3 x+4 y-5=0$. Then the locus of the centroid of $\triangle A B C$ is a line parallel to

If the normal form of the equation of a straight line $4 x+3 y+2=0$ is $x \cos \alpha+y \sin \alpha=p$ and its intercept form is $\frac{x}{a}+\frac{y}{b}=1$, then $\frac{p \sec \alpha}{a b}=$