The latus rectum of a parabola whose focal chord $PSQ$ is such that $SP = 3$ and $SQ = 2$ is given by

The point on the parabola $y^2 = 18x$,for which the ordinate is three times the abscissa,is

Find the equation of the parabola with vertex at $(0, 0)$ and focus at $(0, 2)$.

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

If $(x_1, y_1)$ and $(x_2, y_2)$ are the endpoints of a focal chord of the parabola $y^2 = 4ax$,then what is the square of the $G.M.$ of $x_1$ and $x_2$?

The straight line joining any point $P$ on the parabola $y^2 = 4ax$ to the vertex and the perpendicular from the focus to the tangent at $P$ intersect at $R$. Then the equation of the locus of $R$ is: