What is the vertex of the parabola $x^2 - 8y - x + 19 = 0$?

The shortest distance from $(0,3)$ to the parabola $y^2=4x$ 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?

The line $y = 2x + c$ is tangent to the parabola $y^2 = 4x$,then $c = $

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 $..........$.

If the tangents and normals at the extremities of a focal chord of a parabola $y^2 = 4ax$ intersect at $(x_1, y_1)$ and $(x_2, y_2)$ respectively,then: