What do the equations $x = \frac{t}{4}$ and $y = \frac{t^2}{4}$ represent?

For the parabola $y^2 = 4ax$,what is the $x$-coordinate of the point closest to the focus?

The eccentricity of the parabola $x^2 - 4x - 4y + 4 = 0$ is

From the point $(-1, 2)$,tangent lines are drawn to the parabola $y^2 = 4x$. Find the equation of the chord of contact.

$P$ and $Q$ are two points on the parabola $y^2 = 8x$ and $S$ is its focus. $PS$ and $QS$ meet the curve again in $T$ and $R$ respectively. If $PQ$ passes through a fixed point $(-2, 3)$,then $TR$ also passes through a fixed point whose coordinates are

The length of the normal chord of the parabola $y^2 = 4x$,which makes an angle of $\frac{\pi}{4}$ with the $x$-axis,is: