If the vertex of a parabola is at the origin and the directrix is $x + 5 = 0$,then its latus rectum is

If the point $(a, 2a)$ is an interior point of the region bounded by the parabola $y^2 = 16x$ and the double ordinate through the focus,then

Find the equation of the latus rectum of the parabola $x^2 = -12y$.

Let $P(2,4)$ and $Q(18,-12)$ be the points on the parabola $y^2=8x$. The equation of the straight line having slope $\frac{1}{2}$ and passing through the point of intersection of the tangents to the parabola drawn at the points $P$ and $Q$ is

If $(-1,-1)$ is the focus and $x+y+4=0$ is the directrix of a parabola,then its vertex is

The points $(at_1^2, 2at_1)$,$(at_2^2, 2at_2)$,and $(a, 0)$ will be collinear,if