Tangent to the curve $$y = {x^2} + 6$$ at a point $$(1, 7)$$ touches the circle $${x^2} + {y^2} + 16x + 12y + c = 0$$ at a point $$Q$$. Then the coordinates of $$Q$$ are

The angle between the tangents drawn from the point $$(1, 4)$$ to the parabola $${y^2} = 4x$$ is

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

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