A tangent is drawn to the parabola y² = 6x which is perpendicular to the line 2x + y = 1. Which of the following points does NOT lie on it?

If P is a point on the parabola y = x² + 4 which is closest to the straight line y = 4x $$-$$ 1, then the co-ordinates of P are :

The locus of the mid-point of the line segment joining the focus of the parabola y² = 4ax to a moving point of the parabola, is another parabola whose directrix is :

The centre of the circle passing through the point (0, 1) and touching the parabola
y = x² at the point (2, 4) is :