If the line $y = 2x + k$ is a tangent to the curve $x^2 = 4y$,then $k$ is equal to

How many parabolas can be drawn if the two endpoints of the latus rectum are given?

If $y=mx+1$ is a tangent to the parabola $y^2=4x$,then $m=$

The locus of the middle points of the chords of the parabola $y^2 = 4ax$ which pass through the origin is:

$A$ chord is drawn through the focus of the parabola $y^2 = 6x$ such that its distance from the vertex of this parabola is $\frac{\sqrt{5}}{2}$. Then,its slope can be:

Consider the parabola $y^2=8x$. Let $\Delta_1$ be the area of the triangle formed by the endpoints of its latus rectum and the point $P\left(\frac{1}{2}, 2\right)$ on the parabola,and $\Delta_2$ be the area of the triangle formed by the intersection points of the tangents drawn at $P$ and at the endpoints of the latus rectum. Then $\frac{\Delta_1}{\Delta_2}$ is