If the line ax + by + c = 0 is a tangent to the curve xy = 4, then

S and T are the foci of an ellipse and B is an end point of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is

For different values of $$\alpha$$, the locus of the point of intersection of the two straight lines $$\sqrt 3 x - y - 4\sqrt 3 \alpha = 0$$ and $$\sqrt 3 \alpha x + \alpha y - 4\sqrt 3 = 0$$ is

The eccentricity of the hyperbola $$4{x^2} - 9{y^2} = 36$$ is