$(1, 1)$ 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 $a+b+c+d=$

The length of the latus rectum of the parabola $2\{(x - 1)^2 + (y - 3)^2\} = (x + y - 1)^2$ is:

If the area of the triangle whose one vertex is at the vertex of the parabola,${y^2} + 4(x - {a^2}) = 0$ and the other two vertices are the points of intersection of the parabola and $y$-axis,is $250 \text{ sq. units}$,then a value of $a$ is

If the tangent at a point $P$ on a parabola makes an angle $\alpha$ with its focal distance,then the angle between the tangent and the axis of the parabola is:

If the distances of two points $P$ and $Q$ on the parabola $y^2 = 4ax$ from its focus are $4$ and $9$ respectively,then what is the distance of the point of intersection of the tangents at $P$ and $Q$ from the focus?

$y = 3x - 2$ is a straight line touching the parabola $(y - 3)^2 = 12(x - 2)$. If a line drawn perpendicular to this line at point $P$ on it touches the given parabola,then the point $P$ is: