The line $y=mx+3$ is tangent to the parabola $y^2=4x$,if the value of $m$ is

If the perpendicular distance from the focus of a parabola $y^2=4ax$ to its directrix is $\frac{3}{2}$,then the equation of the normal drawn at $(4a, -4a)$ is

If the focus of a parabola is $(1, 0)$ and its directrix is $x + y = 5$,what is its vertex?

If $a > 0$ and $b^2 - 4ac = 0$,then the curve $y = ax^2 + bx + c$

$A$ beam of light travels along the line $y = -4$ from right to left and strikes a parabola at point $P$. If the focus and directrix of the parabola are $(2, 0)$ and $x = -2$ respectively,then find the coordinates of the point where the reflected beam contacts the parabola again.

The axis of the parabola $x^{2}+2 x y+y^{2}-5 x+5 y-5=0$ is