Tangents at the extremities of any focal chord of a parabola intersect

If the tangents of the parabola $y^2=8x$ passing through the point $P(1,3)$ touch the parabola at $A$ and $B$,then the area (in sq. units) of $\triangle PAB$ is

$A$ circle of radius $4$,drawn on a chord of the parabola $y^2 = 8x$ as diameter,touches the axis of the parabola. Then,the slope of the chord is

$A$ ray of light moving parallel to the $x$-axis gets reflected from a parabolic mirror whose equation is $(y - 2)^2 = 4(x + 1)$. After reflection,the ray must pass through the point:

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

If the vertex of a parabola is at the origin and the directrix is $x + 5 = 0$,then its latus rectum is