On the parabola $y = x^2$,the point at the least distance from the straight line $y = 2x - 4$ is

What is the distance between the focus and the directrix of the parabola $x^2 = -8y$?

Suppose the tangent to the parabola $y=x^2+px+q$ at $(0,3)$ has slope $-1$. Then,$p+q$ equals

The vertex of the parabola $3x - 2y^2 - 4y + 7 = 0$ is

For the parabola $y^2 = 8x$,what is the position of the point $(2, 5)$?

$A$ normal with slope $\frac{1}{\sqrt{6}}$ is drawn from the point $(0, -\alpha)$ to the parabola $x^2 = -4ay$,where $a > 0$. Let $L$ be the line passing through $(0, -\alpha)$ and parallel to the directrix of the parabola. Suppose that $L$ intersects the parabola at two points $A$ and $B$. Let $r$ denote the length of the latus rectum and $s$ denote the square of the length of the line segment $AB$. If $r : s = 1 : 16$,then the value of $24a$ is. . . .