The directrix of the parabola $2 y^2+25 x=0$ 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 . . . . . .

An equilateral triangle is inscribed in the parabola $y^2 = 8x$,with one of its vertices at the vertex of the parabola. Then,the length of the side of that triangle is

If the focal distance of a point $P(2, y_1)$ on the parabola $y^2=kx$ is $3$,then the equation of the tangent drawn at $P$ to the given parabola is

What is the angle subtended by the latus rectum of the parabola $y^2 = ax$ at its vertex?

The equation of the parabola with $(-3, 0)$ as focus and $x + 5 = 0$ as directrix is