The focal distance of the point $(4, 4)$ on the parabola with vertex at $(0, 0)$ and symmetric about the $y$-axis is:

The equation of the directrix of the parabola $x^2+8x+12y+4=0$ is

Let $P_{1}$ be a parabola with vertex $(3,2)$ and focus $(4,4)$,and let $P_{2}$ be its mirror image with respect to the line $x + 2y = 6$. Then the directrix of $P_{2}$ is $x + 2y =$

The area of the triangle formed by the lines joining the vertex of the parabola $x^2=12y$ to the ends of its latus rectum is equal to $...$ sq. units.

$A$ parabola having its axis parallel to the $Y$-axis passes through the points $(0, 2/5)$,$(4, -2)$,and $(1, 8/5)$. Which of the following points lies on this parabola?

Let $PQ$ be a chord of the parabola $y^2=12x$ and the midpoint of $PQ$ be at $(4,1)$. Then,which of the following points lies on the line passing through the points $P$ and $Q$?