If $(2,0)$ is the vertex and the $Y$-axis is the directrix of a parabola,then its focus is

The equation of the parabola with vertex at $(0,0)$ and length of latus rectum equal to $\frac{16}{3}$ is:

Let $A$ and $B$ be two distinct points on the parabola $y^{2}=4x$. If the axis of the parabola touches a circle of radius $r$ having $AB$ as its diameter, then the slope of the line $AB$ is

The points of intersection of the parabolas $y^2=5x$ and $x^2=5y$ lie on the line

If $x + y = K$ is a normal to the parabola $y^2 = 12x$,then what is the value of $K$?

The length of the latus rectum of a parabola whose focal chord $PSQ$ is such that $PS = 3$ and $QS = 2$ is