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 _________.

If the tangent to the curve, y = e^x at a point (c, e^c) and the normal to the parabola, y² = 4x at the point (1, 2) intersect at the same point on the x-axis, then the value of c is ________ .

Let a line y = mx (m > 0) intersect the parabola, y² = x at a point P, other than the origin. Let the tangent to it at P meet the x-axis at the point Q. If area ($$\Delta $$OPQ) = 4 sq. units, then m is equal to __________.