Q.Find the coordinates of the focus, the equation of the directrix, the axis and the length of the latus rectum of the parabola $x^2=-16y$.

A parabola is the locus of a point equidistant from a fixed point, the focus, and a fixed line not through the focus, the directrix -- the defining focus-directrix property that distinguishes it, and the ellipse and hyperbola after it, from the circle's simpler single-distance definition. Applying this property with focus $(a,0)$ and directrix $x=-a$, and equating the two distances via the distance formula, derives the standard equation $y^2=4ax$ directly; three further orientations ($y^2=-4ax$, $x^2=4ay$, $x^2=-4ay$) cover every other choice of axis and opening direction. The vertex is the origin, the axis is the line of symmetry through the vertex and focus, and the latus rectum -- the focal chord perpendicular to the axis -- has length $4a$ in every orientation. Because every point is equidistant from the focus and directrix by definition, the parabola's eccentricity is always exactly $e=1$, a single fixed value unlike the ellipse and hyperbola.