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

The equation of the normal to the parabola $y^2 = 4ax$ at the point $\left( \frac{a}{m^2}, \frac{2a}{m} \right)$ is:

The equation of the parabola whose axis is vertical and passes through the points $(0, 0), (3, 0)$ and $(-1, 4)$ is

The ordinates of the vertices of a triangle inscribed in the parabola $y^2 = 4ax$ are $y_1, y_2, y_3$. Find the area of the triangle.

Find the area of the triangle formed by the tangent and the normal at one end of the latus rectum of the parabola $y^2 = 4ax$ with the axis of the parabola.

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 $x_2$?