Find the equation of the parabola that satisfies the following conditions: Vertex $(0, 0)$,focus $(-2, 0)$.

If the parabola $y^2 = 4ax$ passes through the point $(1, -2)$,then the tangent at this point is

If the points of intersection of the parabolas $y^2=5x$ and $x^2=5y$ lie on the line $L$,then the area of the triangle formed by the directrix of one parabola,the latus rectum of another parabola,and the line $L$ is

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:

The area of the triangle formed by the lines joining the vertex of the parabola,$x^2 = 8y$,to the extremities of its latus rectum is

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 $\sqrt{2}$)?