The focal chord to $${y^2} = 16x$$ is tangent to $${\left( {x - 6} \right)^2} + {y^2} = 2,$$ then the possible values of the slope of the chord, are

If $$a > 2b > 0$$ then the positive value of $$m$$ for which $$y = mx - b\sqrt {1 + {m^2}} $$ is a common tangent to $${x^2} + {y^2} = {b^2}$$ and $${\left( {x - a} \right)^2} + {y^2} = {b^2}$$ is

The equation of the common tangent to the curves $${y^2} = 8x$$ and $$xy = - 1$$ is

The locus of the mid-point of the line segment joining the focus to a moving point on the parabola $${y^2} = 4ax$$ is another parabola with directrix