If the equation of the parabola,whose vertex is at $(5,4)$ and the directrix is $3x+y-29=0$,is $x^{2}+ay^{2}+bxy+cx+dy+k=0$,then $a+b+c+d+k$ is equal to

If tangent lines are drawn from the point $(-1, 2)$ to the parabola $y^2 = 4x$, then the area of the triangle (in sq. units) formed by the chord of contact and the tangents drawn is: (in $\sqrt{2}$)

If tangents are drawn from the point $(-1, 2)$ to the parabola $y^2 = 4x$, what is the area of the triangle formed by the chord of contact and the tangents (in $\sqrt{2}$)?

If $(2 t^2, 4 t)$ is a point on the parabola $y^2 = 8x$ such that its focal distance is $3$,then $t =$

Variable straight lines $y=mx+c$ make intercepts on the curve $y^2-4ax=0$ which subtend a right angle at the origin. Then the point of concurrence of these lines $y=mx+c$ is

$A$ parabola has the origin $(0,0)$ as its focus and the line $x = 2$ as the directrix. Then the vertex of the parabola is at