The directrix of the parabola $2 y^2+25 x=0$ 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

What is the slope of the tangent drawn from the point $(4, 10)$ to the parabola $y^2 = 9x$?

$A$ line passing through the point of intersection of $x+y=4$ and $x-y=2$ makes an angle $\tan^{-1}\left(\frac{3}{4}\right)$ with the $X$-axis. It intersects the parabola $y^{2}=4(x-3)$ at points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$, respectively. Then $|x_{1}-x_{2}|$ is equal to

The smallest value of $x^2 - 3x + 3$ in the interval $(-3, 3/2)$ is

What is the focal distance of a point $(x_1, y_1)$ on the parabola $y^2 = 12x$?