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 :

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

Axis of a parabola lies along x-axis. If its vertex and focus are at distances 2 and 4 respectively from the origin, on the positive x-axis then which of the following points does not lie on it?

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 :