If the focus of a parabola is $(0,-3)$ and its directrix is $y=3$,then its equation is

The equation $y^{2}+4x+4y+k=0$ represents a parabola whose latus rectum is

What is the vertex of the parabola $9x^2 - 6x + 36y + 9 = 0$?

The parabola $x^2=4ay$ makes an intercept of length $\sqrt{40}$ units on the line $y=2x+1$. Find the value of $4a$.

The angle between the two curves $y^2 = 4(x + 1)$ and $x^2 = 4(y + 1)$ is .............. $^\circ$.

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