What is the point of intersection of the latus rectum and the axis of the parabola $y^2 - 4y - 2x - 8 = 0$?

What are the coordinates of the endpoints of the latus rectum of the parabola $(y - 1)^2 = 4(x + 1)$?

The normal at a point on the parabola $y^2=4x$ passes through $(5,0)$. If there are two more normals to this parabola passing through $(5,0)$,then the equation of one of these normals is

If $m$ is the slope of the normal to the parabola $y^2 + 4x + 4y = 0$ at the point $(-3, 2)$,which is one of the endpoints of a focal chord,find the value of $m$.

If $lx + my + n = 0$ is tangent to the parabola $x^2 = y$,then the condition of tangency is

$A$ tangent and a normal are drawn at the point $P(2, -4)$ on the parabola $y^{2} = 8x$,which meet the directrix of the parabola at the points $A$ and $B$ respectively. If $Q(a, b)$ is a point such that $AQBP$ is a square,then $2a + b$ is equal to: