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 :

Let P be the point of intersection of the common tangents to the parabola y² = 12x and the hyperbola 8x² – y² = 8. If S and S' denote the foci of the hyperbola where S lies on the positive x-axis then P divides SS' in a ratio :