If a circle with its centre at the focus of the parabola $y^2=2 p x$ is such that it touches the directrix of the parabola, then a point of intersection of the circle and the parabola is

If the tangent drawn at the point $P(4,8)$ to the parabola $y^2=16 x$ meets the parabola $y^2=16 x+80$ at $A$ and $B$, then the mid-point of $A B$ is

For the parabola $y=\frac{h^3}{3} x^2+\frac{h^2}{2} x-h+\frac{3}{4 h^3}$, if the equation of directrix is $y=k$, then $k: h$

The equation of the common tangent of the parabolas $x^2=108 y$ and $y^2=32 x$ is