If one end of a focal chord $AB$ of the parabola $y^{2}=8x$ is at $A\left(\frac{1}{2},-2\right)$,then the equation of the tangent to it at $B$ is:

If the distances of two points $P$ and $Q$ on the parabola $y^2 = 4ax$ from its focus are $4$ and $9$ respectively,then what is the distance of the point of intersection of the tangents at $P$ and $Q$ from the focus?

If $\theta$ is the acute angle between the tangents drawn from the point $(1,5)$ to the parabola $y^2=9x$,then:

The locus of the feet of the perpendiculars drawn from the vertex of the parabola $y^2 = 4ax$ upon all such chords of the parabola which subtend a right angle at the vertex 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 . . . . . .

If $x-2y+k=0$ is a tangent to the parabola $y^2-4x-4y+8=0$,then the value of $k$ is