What is the length of the latus rectum of the parabola $x^2 = -y$?

From the point $(-1, 2)$,tangent lines are drawn to the parabola $y^2 = 4x$. The area of the triangle formed by the chord of contact and the tangents is given by:

If $x+5=0$ is the directrix and $(-3,0)$ is the vertex of a parabola,then the equation of this parabola is . . . . . .

If the tangent and normal at any point $P$ of a parabola meet the axis of the parabola in $T$ and $G$ respectively,then

The centroid of the triangle formed by joining the feet of the normals drawn from any point to the parabola $y^2 = 4ax$ lies on

If $(x_1, y_1)$ and $(x_2, y_2)$ are the points on the parabola $y^2 = 32x$ each at a focal distance of $10$ units,then $2(x_1^2 + x_2^2 + y_1^2 + y_2^2) = $