The equation of the latus rectum of a parabola is $x + y = 8$ and the equation of the tangent at the vertex is $x + y = 12$. The length of the latus rectum is:

The length of the latus rectum of a parabola,whose vertex and focus are on the positive $x$-axis at a distance $R$ and $S$ $(S > R)$ respectively from the origin,is:

The maximum possible area bounded by the parabola $y=x^2+x+10$ and a chord of the parabola of length $1$ is

Find the equation of the parabola that satisfies the following conditions: Vertex $(0, 0)$,passing through $(5, 2)$,and symmetric with respect to the $y$-axis.

If $5x - 2y + k = 0$ is a tangent to the parabola $y^2 = 6x$,then their point of contact is

Let $x=2t, y=\frac{t^2}{3}$ be a conic. Let $S$ be the focus and $B$ be the point $(0, \alpha)$ on the axis of the conic such that $SA \perp BA$,where $A$ is any point $(2t, \frac{t^2}{3})$ on the conic. If $k$ is the ordinate of the centroid of $\Delta SAB$,then $\lim_{t \rightarrow 1} k$ is equal to