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 :

The area (in sq. units) of the smaller of the two circles that touch the parabola, y² = 4x at the point (1, 2) and the x-axis is :-

If one end of a focal chord of the parabola, y² = 16x is at (1, 4), then the length of this focal chord is :