The normal to the parabola ${y^2 = 8x}$ at the point $(2, 4)$ meets the parabola again at the point

Let $A$ and $B$ be the two points of intersection of the line $y+5=0$ and the mirror image of the parabola $y^2=4x$ with respect to the line $x+y+4=0$. If $d$ denotes the distance between $A$ and $B$,and $a$ denotes the area of $\triangle SAB$,where $S$ is the focus of the parabola $y^2=4x$,then the value of $(a+d)$ is:

Tangents drawn from the point $(-8, 0)$ to the parabola $y^2 = 8x$ touch the parabola at $P$ and $Q$. If $F$ is the focus of the parabola,then the area of the triangle $PFQ$ (in sq. units) is equal to

$(1, 1)$ is the vertex and $x+y+1=0$ is the directrix of a parabola. If $(a, b)$ is its focus and $(c, d)$ is the point of intersection of the directrix and the axis of the parabola,then $a+b+c+d=$

$A$ line passing through the point of intersection of $x+y=4$ and $x-y=2$ makes an angle $\tan^{-1}\left(\frac{3}{4}\right)$ with the $X$-axis. It intersects the parabola $y^{2}=4(x-3)$ at points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$,respectively. Then $|x_{1}-x_{2}|$ is equal to

$A(-1, 3)$ is a fixed point outside the parabola $y^2 = 4ax$ $(a > 0)$ and $P$ is a point moving on the parabola. The locus of point $Q$ which divides $AP$ in the ratio $3:2$ is a conic. Then the focus of that conic is