The equation of the common tangent touching the circle $${\left( {x - 3} \right)^2} + {y^2} = 9$$ and the parabola $${y^2} = 4x$$ above the $$x$$-axis is

If the line $$x - 1 = 0$$ is the directrix of the parabola $${y^2} - kx + 8 = 0,$$ then one of the values of $$k$$ is

If $$x + y = k$$ is normal to $${y^2} = 12x,$$ then $$k$$ is

The curve described parametrically by $$x = {t^2} + t + 1,$$ $$y = {t^2} - t + 1 $$ represents