The maximum number of points on the parabola $y^2 = 16x$ that are equidistant from a variable point $P$ (which lies inside the parabola) is -

$A$ parabola has its focus on the positive $X$-axis and the $Y$-axis as its directrix. If $P(\alpha, 4)$ is a point on this parabola such that the tangent to the parabola at point $P$ passes through the origin, then the distance of $P$ from the origin is

If the focal chord drawn through the point $P(5,5)$ to the parabola $y^2=5x$ meets the parabola again at the point $Q$,then the tangent drawn to this parabola at $Q$ meets the axis of the parabola at the point

Tangents drawn from the point $(-8, 0)$ to the parabola $y^2 = 8x$ touch the parabola at $P$ and $Q$. If $F$ is the focus of the parabola,then the area of the triangle $PFQ$ (in sq. units) is equal to

Statement $-1:$ The line $x - 2y = 2$ meets the parabola $y^2 + 2x = 0$ only at the point $(-2, -2).$
Statement $-2:$ The line $y = mx - \frac{1}{2m}$ $(m \neq 0)$ is tangent to the parabola $y^2 = -2x$ at the point $\left( -\frac{1}{2m^2}, -\frac{1}{m} \right).$

What are the equations of the tangents at the endpoints of the latus rectum of the parabola $y^2 = 4ax$?