If $y=mx+4$ is a tangent to both the parabolas $y^{2}=4x$ and $x^{2}=2by$,then $b$ is equal to:

For the parabola $y^{2} = 4x$,the point $P$ whose focal distance is $17$ is

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

Study the following statements.
$I$. The vertex of the parabola $x = ly^2 + my + n$ is $\left(n - \frac{m^2}{4l}, -\frac{m}{2l}\right)$.
$II$. The focus of the parabola $y = lx^2 + mx + n$ is $\left(-\frac{m}{2l}, n - \frac{m^2-1}{4l}\right)$.
$III$. The pole of the line $lx + my + n = 0$ with respect to the parabola $x^2 = 4ay$ is $\left(-\frac{2al}{m}, \frac{n}{m}\right)$.
Then,the correct option among the following is:

If $Q$ is the point on the parabola $y^2=4x$ that is nearest to the point $P(2,0)$, then $PQ=$

What is the slope of the tangents drawn from $(3, 8)$ to the parabola $y^2 = -12x$?