The locus of the vertices of the family of parabolas
$$y = {{{a^3}{x^2}} \over 3} + {{{a^2}x} \over 2} - 2a$$ is :

In the ellipse, the distance between its foci is $$6$$ and minor axis is $$8$$. Then its eccentricity is :

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length $$x$$. The maximum area enclosed by the park is

The function $$f\left( x \right) = {x \over 2} + {2 \over x}$$ has a local minimum at