Equation of a common tangent to the circle, x² + y² – 6x = 0 and the parabola, y² = 4x is :

If $$\theta $$ denotes the acute angle between the curves, y = 10 – x² and y = 2 + x² at a point of their intersection, the |tan $$\theta $$| is equal to :

Let P be a point on the parabola, x² = 4y. If the distance of P from the center of the circle, x² + y² + 6x + 8 = 0 is minimum, then the equation of the tangent to the parabola at P, is :

Tangent and normal are drawn at P(16, 16) on the parabola y² = 16x, which intersect the axis of the parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B and $$\angle $$CPB = $$\theta $$, then a value of tan$$\theta $$ is :