The length of the latus rectum of the parabola $y^2 - 4y - 2x - 8 = 0$ is:

If a circle with its centre at the focus of the parabola $y^2 = 2px$ is such that it touches the directrix of the parabola,then a point of intersection of the circle and the parabola is

The equation of the parabola with vertex at $(0,0)$ and length of latus rectum equal to $\frac{16}{3}$ is:

If a parabola passes through the points $(-2, 1)$,$(1, 2)$,and $(-1, 3)$ and has a horizontal axis,then the length of the latus rectum of that parabola is:

$A$ point $P(x, y)$ moves such that its distance from the point $(a, 0)$ is always equal to its distance from the line $x + a = 0$. The locus of the point is:

The focus of the parabola $y^2 = 4y - 4x$ is