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

If the normals at points $t_1$ and $t_2$ on the parabola $y^2 = 4ax$ intersect again on the parabola,then what is the value of $t_1t_2$?

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

An equilateral triangle is inscribed in the parabola $y^2=16ax$ with one of its vertices at the origin. Then,the centroid of that triangle is

The vertex of the parabola is at $(1, 2)$ and its axis is parallel to the $y$-axis. If the parabola passes through $(0, 6)$,then its latus rectum is:

If a circle with its centre at the focus of the parabola $y^2 = 2px$ is such that it touches the directrix of the parabola,then a point of intersection of the circle and the parabola is