Two parabolas with a common vertex and with axes along x-axis and $$y$$-axis, respectively intersect each other in the first quadrant. If the length of the latus rectum of each parabola is $$3$$, then the equation of the common tangent to the two parabolas is :

If y = mx + c is the normal at a point on the parabola y² = 8x whose focal distance is 8 units, then $$\left| c \right|$$ is equal to :

If the common tangents to the parabola, x² = 4y and the circle, x² + y² = 4 intersect at the point P, then the distance of P from the origin, is :

P and Q are two distinct points on the parabola, y² = 4x, with parameters t and t₁ respectively. If the normal at P passes through Q, then the minimum value of $$t_1^2$$ is :