What is the equation of the normal to the curve $y^2 = 16x$ at the point $(1, 4)$?

Let the tangent to the curve $x^2+2x-4y+9=0$ at the point $P(1,3)$ on it meet the $y$-axis at $A$. Let the line passing through $P$ and parallel to the line $x-3y=6$ meet the parabola $y^2=4x$ at $B$. If $B$ lies on the line $2x-3y=8$,then $(AB)^2$ is equal to $............$.

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

The focal distance of a point $(5, 5)$ on the parabola $x^2 - 2x - 4y + 5 = 0$ is

Let the focal chord $PQ$ of the parabola $y^2=4x$ make an angle of $60^{\circ}$ with the positive $x$-axis,where $P$ lies in the first quadrant. If the circle,whose one diameter is $PS$,$S$ being the focus of the parabola,touches the $y$-axis at the point $(0, \alpha)$,then $5 \alpha^2$ is equal to :

If the tangent to the parabola $y^{2} = 4ax$ at point $P(p, q)$ is perpendicular to the tangent at another point $Q$,find the coordinates of $Q$.