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

If the line $lx + my + n = 0$ is a tangent to the parabola $y^2 = 4ax$,then the locus of its point of contact is

Find the equation of the tangent at the vertex of the parabola $4y^2 + 6x = 8y + 7$.

The shortest distance between the line $y-x=1$ and the curve $x=y^2$ is

For the parabola $y^2 = 8x$,what is the position of the point $(2, 5)$?

Let $P(x, y)$ be the midpoint of the line joining $(1, 0)$ to a point on the curve $y^{2} = \left|\begin{array}{ll}x+1 & x+2 \\ x+3 & x+5\end{array}\right|$. Then,the locus of $P$ is symmetrical about