### Parabola

goals
If point P is $(a{t^2},2at)$,then the length of the focal chord PQ is
$a{\left( {t + \cfrac{1}{t}} \right)^2}$.
The equation of the normal to the parabola, $x^{2}=8y$ at $x=4$ is:
The shortest distance between the line $y-x-1$ and the curve $x={y}^{2}$
An arc is in the form of parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m form the vertex of the parabola
The polar of the point $(2,1)$ with respected to the parabola $y^2 = 6x$, is