The parametric equations of the parabola $y^2-4x-8y-12=0$ are

If the lines $2x + 3y + 12 = 0$ and $x - y + k = 0$ are conjugate with respect to the parabola $y^2 = 8x$,then $k$ is equal to

Let $P(4, 4\sqrt{3})$ be a point on the parabola $y^2 = 4ax$ and $PQ$ be a focal chord of the parabola. If $M$ and $N$ are the feet of the perpendiculars drawn from $P$ and $Q$ respectively on the directrix of the parabola,then the area of the quadrilateral $PQMN$ is equal to:

If the tangent to the parabola $y^{2} = 4ax$ at point $P(p, q)$ is perpendicular to the tangent at another point $Q$,find the coordinates of $Q$.

Normals are drawn from the point $P(8,0)$ to the parabola $y^2=12x$. If $\theta$ is the acute angle between two non-horizontal normals among them,then $\tan \theta=$

The area of the triangle formed by the lines joining the vertex of the parabola $x^2 = 48y$ to the ends of its latus rectum is .....