The locus of a point which divides the line segment joining the point (0, –1) and a point on the parabola, x² = 4y, internally in the ratio 1 : 2, is :

If y = mx + 4 is a tangent to both the parabolas, y² = 4x and x² = 2by, then b is equal to :

The tangents to the curve y = (x – 2)² – 1 at its points of intersection with the line x – y = 3, intersect at the point :

The equation of common tangent to the curves y² = 16x and xy = –4, is :