For the parabola $y^2 = 4ax$,what is the $x$-coordinate of the point closest to the focus?

Find the equation of the parabola with focus $(0, -3)$ and directrix $y = 3$.

If the parabola $y = \alpha x^{2} - 6x + \beta$ passes through the point $(0, 2)$ and has its tangent at $x = \frac{3}{2}$ parallel to the $X$-axis,then:

The focus of the conic $x^{2}-6x+4y+1=0$ is

If the focus of a parabola is $(1, 0)$ and its directrix is $x + y = 5$,what is its vertex?

What is the length of the latus rectum of the parabola $x^2 = -y$?