$A(2,0), B(0,2), C(-2,0)$ are three points. Let $a, b, c$ be the perpendicular distances from a variable point $P$ on to the lines $A B, B C$ and $C A$ respectively. If $a, b, c$ are in arithmetic progression, then the locus of $P$ is

Two families of lines are given by $a x+b y+c=0$ and $4 a^2+9 b^2-c^2-12 a b=0$. Then, the line common to both the families is

Two non-parallel sides of a rhombus are parallel to the lines $x+y-1=0$ and $7 x-y-5=0$. If $(1,3)$ is the centre of the rhombus and one of its vertices $A(\alpha, \beta)$ lies on $15 x-5 y=6$, then one of the possible values of $(\alpha+\beta)$ is

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