Let E be an ellipse whose axes are parallel to the co-ordinates axes, having its center at (3, $$-$$4), one focus at (4, $$-$$4) and one vertex at (5, $$-$$4). If mx $$-$$ y = 4, m > 0 is a tangent to the ellipse E, then the value of 5m² 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 _____________.

Let L be a common tangent line to the curves

4x² + 9y² = 36 and (2x)² + (2y)² = 31. Then the

square of the slope of the line L is __________.