The diameter of a parabola is . . . . . .

The equation of the parabola with its vertex at the origin,axis on the $y$-axis and passing through the point $(6, -3)$ is

If the vertex of a parabola is $(2, 0)$ and the $y$-axis is its directrix,find its focus.

The length of the latus rectum of the parabola $169\{(x-1)^2+(y-3)^2\}=(5x-12y+17)^2$ is

Let $A(0,1)$,$B(1,1)$,and $C(1,0)$ be the mid-points of the sides of a triangle with incentre at the point $D$. If the focus of the parabola $y^2 = 4ax$ passing through $D$ is $(\alpha + \beta \sqrt{2}, 0)$,where $\alpha$ and $\beta$ are rational numbers,then $\frac{\alpha}{\beta^2}$ is equal to

If $(0, 4)$ and $(0, 2)$ are the vertex and focus of a parabola respectively,then what is its equation?