The focus of the parabola $x^2 = -16y$ is

The line $y = 6x + 1$ touches the parabola $y^2 = 24x$. The coordinates of a point $P$ on this line,from which the tangent to $y^2 = 24x$ is perpendicular to the line $y = 6x + 1$,is

If the focus of a parabola is $(0,-3)$ and its directrix is $y=3$,then its equation is

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

The equation of the tangent at a point $P(t)$,where $t$ is any parameter,to the parabola $y^2 = 4ax$ is:

Let $A, B$ and $C$ be the vertices of a variable right-angled triangle inscribed in the parabola $y^2 = 16x$. Let the vertex containing the right angle be $C = (4, 8)$ and the locus of the centroid of $\triangle ABC$ be a conic $C_o$. Then three times the length of the latus rectum of $C_o$ is . . . . . .