What is the equation of the directrix of the parabola $x^2 = -ay$?

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

The focal distance of a point $(5, 5)$ on the parabola $x^2 - 2x - 4y + 5 = 0$ is

The equation of the lines joining the vertex of the parabola $y^2 = 6x$ to the points on it whose abscissa is $24$ is:

The number of common tangents to the parabolas $y = x^{2}$ and $y = -x^{2} + 4x - 4$ is:

If $b$ and $c$ are the lengths of the segments of any focal chord of a parabola $y^2 = 4ax$,then the length of the semi-latus rectum is: