If $x-2 y+k=0$ is a tangent to the parabola $y^2-4 x-4 y+8=0$, then the value of $k$ is

If the points of intersection of the parabolas $y^2=5 x$ and $x^2=5 y$ lie on the line $L$, then the area of the triangle formed by the directrix of one parabola, latus rectum of another parabola and the line $L$ is

If the line $x \cos \alpha+y \sin \alpha=2 \sqrt{3}$ is a tangent to the ellipse $\frac{x^2}{16}+\frac{y^2}{8}=1$ and $\alpha$ is an acute angle, then $\alpha=$

If $x+\sqrt{3} y=3$ is the tangent to the ellipse $2 x^2+3 y^2=k$ at a point $P$, then the equation of the normal to this ellipse at $P$ is