If the focus of a parabola is $(3, 0)$ and the length of its latus rectum is $8$,what is its vertex?

If $(2, -8)$ is one endpoint of a focal chord of the parabola $y^{2} = 32x$,what is the other endpoint?

Let $S$ be the set of all $a \in \mathbb{N}$ such that the area of the triangle formed by the tangent at the point $P(b, c)$,where $b, c \in \mathbb{N}$,on the parabola $y^2 = 2ax$ and the lines $x = b$ and $y = 0$ is $16 \text{ unit}^2$. Then $\sum_{a \in S} a$ is equal to $..........$.

What are the equations of the tangents at the endpoints of the latus rectum of the parabola $y^2 = 4ax$?

If $x + by + c = 0$ is a normal to the parabola $y^2 = 12x$,then the complete set of all values of $c$ is -

The point of intersection of tangents at the ends of the latus rectum of the parabola $y^2 = 4x$ is