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

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 :

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 :

If the line ax + y = c, touches both the curves x² + y² = 1 and y² = 4$$\sqrt 2 $$x , then |c| is equal to :