A straight line passing through a fixed point $(-3,4)$ intersects the coordinate axes at $A$ and $B$. If $O$ is the origin and $O A B C$ forms a rectangle, then the locus of $C$ is

When the origin is shifted to the point $P$ by translation of axes, the equation $2 x^2+y^2-4 x+4 y=0$ is transformed to $2 x^2+y^2-8 x+8 y+18=0$. Then, the transformed equation of the straight line $x+2 y+2=0$, if the origin is shifted to the same point $P$ is

If the lines $x+y-1=0, k x+2 y+1=0$ and $4 x+2 k y+7=0$ are concurrent, then $k=$

If $\alpha, \beta(\alpha>\beta)$ are two values of $k$ such that the equations $2 x+(3-2 k) y+(2 k+1)=0$ and $k x+(k-1) y-4=0$ represents two perpendicular lines, then $\alpha^2+2 \beta=$