What is the equation of the chord of contact drawn from the point $(2, 4)$ to the parabola $y^2 = 4x$?

The equation of the parabola with the focus $(3,0)$ and the directrix $x+3=0$ is:

$TP$ and $TQ$ are tangents of the parabola $y^2 = 8x$ at $P$ and $Q$ respectively. If the chord $PQ$ passes through the point $(-2, 3)$ and the locus of point $T$ is $y = mx + c$,then $(m + c)$ is equal to -

Two parabolas with a common vertex at the origin and with axes along the $x-$ axis and $y-$ axis,respectively,intersect each other in the first quadrant. If the length of the latus rectum of each parabola is $3$,then the equation of the common tangent to the two parabolas is?

Find the shortest distance of the point $(0, c)$ from the parabola $y=x^{2}$ where $0 \leq c \leq 5$.

The intercepts of the focal chord (which is a part of the latus rectum) to the parabola $y^{2}=4ax$ are $b$ and $k$. Then $k$ is equal to: