A tangent line L is drawn at the point (2, $$-$$4) on the parabola y² = 8x. If the line L is also tangent to the circle x² + y² = a, then 'a' is equal to ___________.

If the point on the curve y² = 6x, nearest to the point $$\left( {3,{3 \over 2}} \right)$$ is ($$\alpha$$, $$\beta$$), then 2($$\alpha$$ + $$\beta$$) is equal to _____________.

Let y = mx + c, m > 0 be the focal chord of y² = $$-$$ 64x, which is tangent to (x + 10)² + y² = 4. Then, the value of 4$$\sqrt 2 $$ (m + c) is equal to _____________.

A line is a common tangent to the circle (x $$-$$ 3)² + y² = 9 and the parabola y² = 4x. If the two points of contact (a, b) and (c, d) are distinct and lie in the first quadrant, then 2(a + c) is equal to _________.