The curve described parametrically by $x = t^2 - 2t + 2$ and $y = t^2 + 2t + 2$ represents:

The shortest distance from $(0,3)$ to the parabola $y^2=4x$ is

The length of the chord of the parabola $y^{2}=4ax$ $(a>0)$ which passes through the vertex and makes an acute angle $\alpha$ with the axis of the parabola is

The equation of the directrix of the parabola $3x^{2} = 16y$ is

The point of intersection of the latus rectum and axis of the parabola $y^2+4x+2y-8=0$ is

Tangent and normal are drawn at $P(16, 16)$ on the parabola ${y^2} = 16x$,which intersect the axis of the parabola at $A$ and $B$,respectively. If $C$ is the centre of the circle through the points $P, A$ and $B$ and $\angle CPB = \theta$,then a value of $\tan \theta$ is: