A common tangent to the circle $x^2+y^2=9$ and parabola $y^2=8 x$ is

The normal drawn at a point $(2,-4)$ on the parabola $y^2 \pm 8 x$ cuts again the same parabola at $(\alpha, \beta)$, then $\alpha+\beta=$

If the axes are rotated through an angle $45^{\circ}$ about the origin in anticlockwise direction, then the transformed equation of $y^2=4 a r$ is

The line $x-2 y-3=0$ cuts the parabola $y^2=4 \operatorname{ar}$ at the points $P$ and $Q$. If the focus of this parabola is $\left(\frac{1}{4}, k\right)$. then $P Q=$