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 :

The tangent to the parabola y² = 4x at the point where it intersects the circle x² + y² = 5 in the first quadrant, passes through the point :