If the normals at points $t_1$ and $t_2$ on the parabola $y^2 = 4ax$ intersect again on the parabola,then what is the value of $t_1t_2$?

The ends of the latus rectum of the conic ${x^2} + 10x - 16y + 25 = 0$ are

What are the parametric equations of the parabola $(y - 2)^2 = 12(x - 4)$?

The equation of a tangent to the parabola $y^2 = 8x$ is $y = x + 2$. If another tangent is drawn to the parabola from a point on this line such that it is perpendicular to the given tangent,find the point.

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

An arch is in the form of a parabola with its axis vertical. The arch is $10 \, m$ high and $5 \, m$ wide at the base. How wide is it $2 \, m$ from the vertex of the parabola (in $, m$)?